CN111552178B - Aircraft stand waiting and pushing control method with controllable repeat request time interval - Google Patents

Aircraft stand waiting and pushing control method with controllable repeat request time interval Download PDF

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CN111552178B
CN111552178B CN202010326378.6A CN202010326378A CN111552178B CN 111552178 B CN111552178 B CN 111552178B CN 202010326378 A CN202010326378 A CN 202010326378A CN 111552178 B CN111552178 B CN 111552178B
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aircraft
stand
taxiway
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waiting
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CN111552178A (en
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廉冠
李文勇
王涛
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Guilin University of Electronic Technology
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Abstract

The invention discloses an aircraft stand waiting push-out control method with controllable repeat request time intervals, which provides a linear control push-out strategy, wherein the strategy can dynamically adjust push-out frequency according to the state on a taxiway, so that the push-out frequency is reduced along with the increase of the queuing length of the taxiway, the aircraft which is refused to be pushed out is required to temporarily wait at the stand, and the push-out is applied again after a period of time, and the total cost of the departure of the aircraft is reduced by optimizing the relationship between fuel oil cost and stand waiting cost. And further, solving the model by using an iterative optimization algorithm based on a continuous time Markov chain to solve the optimal restitution time interval, the optimal taxiway queuing length threshold and the optimal total cost of departure operation, thereby providing more intelligent and efficient control decision for airport operation.

Description

Aircraft stand waiting and pushing control method with controllable repeat request time interval
Technical Field
The disclosure relates to the technical field of airport scene operation scheduling, in particular to an aircraft stand waiting and pushing control method with controllable repeat application time intervals.
Background
The start of push-out to take-off of a free tow vehicle during aircraft departure is known as the taxiing process, which consumes fuel, while at hub airports, particularly during peak departure periods, aircraft often experience long waiting lines on taxiways, resulting in increased fuel costs. Under the condition that the airport resource amount is increased without expanding an airport at present, a novel release control means is urgently needed to reduce the fuel consumption cost of departure. Patent CN110134017A discloses an aircraft launch frequency control method, in which the aircraft launch control reapplication time interval is set as a fixed value, i.e. an average service time value, and the control effect thereof cannot adjust the reapplication time interval according to the actual control conditions of different airports, and the cost of aircraft departure is high.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an aircraft stand waiting push-out control method with controllable repeat application time intervals so as to solve the problem that the departure fuel cost is increased due to the fact that aircrafts wait in a taxi way for a long time in a queuing mode.
The technical scheme for realizing the purpose of the invention is as follows:
an aircraft stand wait launch control method with a controllable repeat request time interval, comprising the steps of:
1) according to the departure operation characteristics of the aircraft, proposing the assumed conditions of modeling the departure control process of the aircraft; the aircraft departure operation characteristics comprise weather, queuing forms and takeoff interval characteristics;
2) establishing an aircraft push-out frequency control rule which linearly decreases along with the increase of the taxiway queuing saturation, wherein the taxiway queuing saturation is the ratio of the current taxiway queuing length value to the taxiway queuing length threshold value;
3) determining a punishment rule of the waiting cost of the aircraft stand according to the maximum waiting time of the stand of the aircraft allowed in the airport and the fuel consumption cost of the aircraft in the unit time in the process of sliding;
4) establishing a derived frequency control model according to the fuel consumption cost and the waiting cost of the aircraft parking space;
5) abstracting the push-out process of the push-out frequency control model into a retry M/M/1/K queuing process with variable input rate, wherein the state in the queuing process comprises the following steps: respectively calculating the expectation of the key index of the stand waiting state, the expectation of the key index of the taxiway queuing state, the expectation of the key index of the taxiway waiting time, the expectation of the effective push-out rate and the expectation of the push-out request time interval;
6) solving the push-out frequency control model in a cyclic iterative search mode by combining the expectation of the stand waiting time, the expectation of the taxiway waiting time, the expectation of the effective push-out rate and the expectation of the push-out restitution time interval to obtain an optimal push-out frequency control expression, and controlling the push-out frequency of the aircraft according to the optimal push-out frequency control expression;
in step 3), theThe method for determining the punishment rule of the waiting cost of the aircraft stand comprises the steps of selecting an exponential function to represent the punishment of the waiting cost of the aircraft stand, wherein the expression of the punishment of the waiting cost of the aircraft stand is as follows:
Figure GDA0003735126800000021
wherein β ═ ln (cG) max +1)]/G max C is the fuel consumption cost per unit time of the coasting process, G max The maximum allowable waiting time for the stand;
in step 4), the expression of the derived frequency control model is as follows:
Figure GDA0003735126800000022
wherein C is T For the total cost of aircraft departure, M is the total number of aircraft requested, j is the departure aircraft index, E [ W ] j ]Beta is an expectation of taxiway waiting time of the jth departure aircraft, and is a stand waiting penalty coefficient; g j For the stand waiting time of the jth departing aircraft, EG j ]Expectation of stand waiting time for the jth departure aircraft;
in step 6), the deducing a frequency control expression comprises:
the actual derived frequency:
Figure GDA0003735126800000023
service rate: mu.s
Reissue interval: t is t r
Where λ' is the actual derived frequency; lambda is the frequency of application; n is the current taxiway queuing value; n is a taxiway queuing length threshold, and N/N is taxiway queuing saturation;
recording the average departure time interval of the aircraft, namely the service time as t t When the ratio of the repeat request time interval to the average departure time interval of the aircraft is given as g, g is t r /t t To facilitate the following calculation, the value of g is counted downThe number h is 1/g; the method for selecting the repeat request time interval is given as g-1, g>1 or g<1.
The method for selecting the reiteration time interval includes establishing a state transition equation set when g is 1, wherein for the taxiway queue, the established state transition equation set includes:
λπ 0 ＝μπ 1 (1)
λπ M-1 ＝μπ M (2)
Figure GDA0003735126800000031
Figure GDA0003735126800000032
wherein pi i I is the probability when the system is in state i, i ═ 0,1,2,3, ·, N;
at this time, any state pi i Can be written as to 0 Is represented by the regular equation:
Figure GDA0003735126800000033
obtaining:
Figure GDA0003735126800000034
wherein
Figure GDA0003735126800000035
According to the calculation method of the length of the queue and the stay time of the queuing system, the expectation of the value of the length of the taxiway queue is as follows:
Figure GDA0003735126800000036
wherein:
Figure GDA0003735126800000037
Figure GDA0003735126800000038
the effective push-out rate is expected to be:
Figure GDA0003735126800000039
thus, the taxiway latency expectations are:
Figure GDA00037351268000000310
when the stand waiting state of the computer is calculated, the method comprises the following steps:
A. when n is more than or equal to 0 and less than or equal to M, applying for the aircraft to be deduced with 1 probability, and then E [ G | k ═ n ] ═ 0;
B. when M is more than N and less than or equal to N, recording C aj For the number of times the jth aircraft in the stand queue applies,
for the 1 st aircraft, there is a state transfer function:
Figure GDA0003735126800000041
Figure GDA0003735126800000042
…
Figure GDA0003735126800000043
obtaining the waiting and repeat request times of the 1 st aircraft stand according to the relation between the state and the state probability,
the expectation of the waiting time of the stand is as follows:
Figure GDA0003735126800000044
for the 2 nd aircraft, the expectation of the stand waiting time of the aircraft is related to the expectation of the number of times of application of the 1 st aircraft, and the expectation is as follows:
Figure GDA0003735126800000045
fifthly, for the nth G An airborne vehicle with stand-off latency expectations of:
Figure GDA0003735126800000046
the stand wait time for any one aircraft is expected to be:
Figure GDA0003735126800000047
when g is greater than 1, a state transition equation set is established, and equations in the state transition equation set comprise:
note C b1 The number of repeat requests of the 1 st aircraft in the queue is waited for the parking space, C is obtained b1 The probability of (c) is:
Figure GDA0003735126800000051
Figure GDA0003735126800000052
Figure GDA0003735126800000053
…
Figure GDA0003735126800000054
when the taxiway queuing length n is 0, the first aircraft in the stand waiting queue enters the taxiway with the probability of 1, and then the first aircraft in the stand waiting queue enters the taxiway
Figure GDA0003735126800000055
Obtaining the stand waiting time expectation E [ C ] of the 1 st aircraft by a probability transfer equation b1 ]The expression of (a) is:
Figure GDA0003735126800000056
due to the fact that
Figure GDA0003735126800000057
As the g value changes, the 2 nd aircraft may not be able to operate at t t When the application is deduced at integral multiple of the time, the pair E [ C ] is b1 ]Is corrected, to
Figure GDA0003735126800000058
Comprises the following steps:
Figure GDA0003735126800000059
Figure GDA00037351268000000510
wherein
Figure GDA00037351268000000511
For the 2 nd and m th aircraft, the number of times of waiting for restitution of the aircraft stand is expected to be as follows:
Figure GDA00037351268000000512
Figure GDA00037351268000000513
for the mth aircraft in the stand waiting queue, the total number of applications for push-out is expected to be E [ C ] am ]＝E[C bm ]+ m, containing the initial application, assuming the initial application obeys [0, t ] r ]With even distribution of the above, the stand wait time is expected to be
Figure GDA0003735126800000061
Said method of selecting a reiterated time interval is given as g<1, and
Figure GDA0003735126800000062
when the number of reassessment times is recorded as k, the quotient of k/h is recorded as u k The remainder v k For the 1 st aircraft in the stand waiting queue, the following transition probability state equation exists:
when k is 1, u k ＝0，v k When 1, then:
Figure GDA0003735126800000063
when the k is equal to 2, the reaction condition is as follows,
Figure GDA0003735126800000064
the probability expression for the number of restitution times k is:
Figure GDA0003735126800000065
solving a transition probability state equation to obtain for the 1 st aircraft in the stand queue:
Figure GDA0003735126800000066
by
Figure GDA0003735126800000067
Property of (1), record
Figure GDA0003735126800000068
Quotient of u m The remainder is v m The derivation process is the same as the derivation process of the 1 st aircraft, then
Figure GDA0003735126800000069
Preamble aircraft
Figure GDA00037351268000000610
The conditional probability expression of (a) is:
Figure GDA00037351268000000611
because it is difficult to directly calculate the residual conditional probability expression, a recursive unified algorithm is adopted, and the recursive unified algorithm comprises the following steps of converting the conditional probability of the next sequence into the expression related to the previous sequence:
for the 2 nd aircraft in the stand waiting queue, the stand waiting repeat request times are as follows:
Figure GDA0003735126800000071
for the mth aircraft in the stand waiting queue, there are:
Figure GDA0003735126800000072
and
Figure GDA0003735126800000073
establishing a state transition equation set, wherein equations in the state transition equation set include:
for the mth aircraft in the stand waiting queue, the total number of applications for release is expected to be E C am ]＝E[C bm ]+ m, containing the initial application, assuming the initial application obeys [0, t ] r ]Then the stand wait time is expected to be:
Figure GDA0003735126800000081
said method of selecting a reiterated time interval is given as g<1, and
Figure GDA0003735126800000082
when k is the number of repeat requests,
Figure GDA0003735126800000083
The quotient k/d is u k The remainder is v k ，
Figure GDA0003735126800000084
Quotient of u m Remainder is v m For the 1 st aircraft in the stand waiting queue, the probability expression for restating that the number of times is k is as follows:
Figure GDA0003735126800000085
the number of times the aircraft stands waiting for reiteration for this aircraft is expected to be:
Figure GDA0003735126800000086
derived from the conditional probabilities of the preceding aircraft:
Figure GDA0003735126800000087
derived from a recursive unified algorithm:
Figure GDA0003735126800000088
Figure GDA0003735126800000091
converting the expression into the conditional probability relation between the 2 nd aircraft and any aircraft and the 1 st aircraft in the stand waiting queue:
Figure GDA0003735126800000092
and
Figure GDA0003735126800000093
for the mth aircraft in the stand waiting queue, the total number of applications for push-out is expected to be E [ C ] am ]＝E[C bm ]+ m, containing the initial application, assuming the initial application obeys [0, t ] r ]Then the stand wait time is expected to be:
Figure GDA0003735126800000094
in step 6), solving the derived frequency control model in a loop iteration search manner includes the following steps:
6-1) inputting a data set of a planned application release moment of an aircraft s;
6-2) inputting a reapplication push-out interval time;
6-3) judging that g belongs to the type of g ═ 1, g >1 and g < 1;
6-4) sequencing all the aircraft push-out sequences according to the ascending sequence of application time;
6-5) initializing taxiway queue length threshold N for aircraft s s ；
6-6) applying for release from the tower by the aircraft j, and marking the time when the aircraft j applies for release;
6-7) judging whether the current taxiway queuing length n when the aircraft j applies for release meets n<N s If yes, continuing; if not, marking the state of the aircraft j as stand waiting and judging the waiting time G of the current aircraft j at the stand i If the number of taxiways is larger than the preset value, updating the taxiway queuing length threshold value to be N s +1, over t r After the time period, repeating the application of the aircraft j to the tower, marking the application time of the aircraft j, and judging whether the current taxiway queuing length n of the aircraft j meets n<N s + 1; if not, judging whether the pushed application aircraft index j of the aircraft j meets j or not<M, wherein M represents the maximum value of the aircraft index requested to be released, if yes, the aircraft index requested to be released is updated to be j +1, the aircraft j +1 applies to be released to a tower, the time when the aircraft j +1 applies to be released is marked, and if not, the taxiway fuel cost, the stand waiting penalty cost and the total cost release value C of the aircraft j are calculated Tj ；
6-8) triggering a probability simulation mechanism to judge the random number R j Whether E (0,1) satisfies R j <(1-n/N s ) If so, agreeing to the release application of the aircraft j, marking the position of the aircraft j as a taxiway queue, recording the taxiway waiting time of the aircraft j, and continuing; if not, marking the state of the aircraft j as the stand waiting and judging the waiting time G of the current aircraft j at the stand i If the number of taxiways is larger than the preset value, updating the taxiway queuing length threshold value to be N s +1, repeating the steps of applying for release from the tower by the aircraft j and marking the time of applying for release, and judging whether the taxiway queuing length n of the aircraft j meets n<N s +1；
6-9) judging whether the pushing of all the aircrafts in the time window is finished or not, including judging whether the pushing application aircraft index j of the aircraft j meets j or not<M, wherein M represents the maximum value of the proposed aircraft index, and if so, the maximum value is furtherNewly-released application aircraft index is j +1, the aircraft j +1 applies for release from a tower, the time when the aircraft j +1 applies for release is marked, and if not, the taxiway fuel cost, the stand waiting penalty cost and the release total cost value C of the aircraft j are calculated Tj ；
6-10) determining taxiway queuing length threshold N for aircraft j s Whether or not N is satisfied s <N max Wherein, N is max A maximum value representing a taxiway queue length threshold; if yes, updating the taxiway queuing length threshold to be N s + 1; if not, continuing;
6-11) calculating N s Corresponding to the sum C of derived total cost values Ts Comparing all of said calculated extrapolated total cost values C Ts Outputting the minimum deducing total cost value C Ts ；
6-12) updating the release application interval time, jumping to the step 6-3), and judging the ratio g of the release application interval time to the service time interval k Whether or not g is satisfied k <g max If yes, continuing; if not, calculating the current g value to push down the optimal total cost value C Tg ；
6-13) comparing all of said calculated extrapolated total cost values C Tg Outputting the minimum deducing total cost value C T * As an optimal extrapolated total cost value.
The deduced frequency control expression is obtained by obtaining a taxiway queuing length threshold value, an average stand waiting time, an average taxiway sliding time and an optimal deduced restitution time interval corresponding to the optimal deduced total cost value according to the optimal deduced total cost value, substituting the optimal deduced total cost value and the corresponding taxiway queuing length threshold value, the average stand waiting time, the average taxiway sliding time and the deduced restitution time interval into the deduced frequency control model.
In the step 1), the departure operation characteristics of the aircraft refer to preprocessing the acquired airport departure data and converting the format of the acquired data set at the moment of plan application release into a minute system; the assumed conditions for modeling the aircraft launch control process comprise: ignoring the effects of meteorological conditions, the launch phase performed by the tow vehicle consumes no fuel and therefore does not take into account the taxi time of the aircraft, which is subject to first come first served regulations.
The invention provides an aircraft stand waiting and pushing control method with controllable repeat request time interval, which provides a linear control pushing strategy, wherein the strategy can dynamically adjust the pushing frequency according to the state on a taxiway, so that the pushing frequency is reduced along with the increase of the queuing length of the taxiway, the aircraft which is refused to be pushed out is required to temporarily wait at the stand, and the pushing is applied again after a period of time, the total cost of departure of the aircraft is reduced by optimizing the relation between the fuel cost and the waiting cost of the stand, meanwhile, the dynamic pushing model with the controllable repeat request time interval is utilized, the model is further solved by an iterative optimization algorithm based on a continuous time Markov chain, so as to solve the optimal repeat request time interval, the optimal taxiway queuing length threshold value and the optimal total cost of departure operation, compared with the prior art, the method can reduce the queuing waiting time of the aircrafts on the taxiways on the premise of ensuring the utilization rate of the taxiways and runways, and reduce the fuel cost and the total departure operation cost.
Drawings
Fig. 1 is a flowchart of solving a derived frequency control model by using an iterative optimization algorithm based on a continuous-time markov chain in an embodiment of the present invention.
Detailed Description
The invention will be further elucidated with reference to the drawings and examples, without however being limited thereto.
Example (b):
an aircraft stand waiting push-out control method with controllable repeat request time intervals comprises the following steps:
1) preprocessing the acquired departure data of a certain large hub airport in China, converting the format of the acquired data set at the time of plan application release into a minute system, and providing the assumed conditions of modeling the release control process of the aircraft departure according to the departure operation characteristics of the aircraft, wherein the assumed conditions comprise: neglecting the influence of meteorological conditions, the fuel oil is not consumed in the pushing-out stage completed by the tractor, so the consumed time does not account for the sliding time of the aircraft, and the pushing-out of the aircraft follows the first-come-first-serve rule; the departure operation characteristics of the aircraft comprise weather, queuing forms, takeoff intervals and the like;
2) establishing an aircraft push-out frequency control rule which linearly decreases along with the increase of the taxiway queuing saturation, wherein the taxiway queuing saturation is the ratio of the current taxiway queuing length value to the taxiway queuing length threshold value;
3) determining a punishment rule of the waiting cost of the aircraft stand according to the maximum waiting time of the stand of the aircraft allowed in the airport and the fuel consumption cost of the aircraft in the unit time in the process of sliding;
4) establishing a frequency control model according to the fuel consumption cost and the waiting cost of the aircraft stand;
5) abstracting the push-out process of the push-out frequency control model into a retry M/M/1/K queuing process with variable input rate, wherein the state in the queuing process comprises the following steps: respectively calculating the expectation of key indexes of the stand waiting state, the expectation of key indexes of the taxiway waiting state, the expectation of effective deducing rate and the expectation of deducing a repeat application time interval;
6) solving the push-out frequency control model in a cyclic iterative search mode by combining the expectation of the stand waiting time, the expectation of the taxiway waiting time, the expectation of the effective push-out rate and the expectation of the push-out restitution time interval to obtain an optimal push-out frequency control expression, and controlling the push-out frequency of the aircraft according to the optimal push-out frequency control expression;
in step 3), the aircraft stand waiting cost penalty rule is determined by selecting an exponential function to represent the penalty of the aircraft stand waiting cost, and the expression of the penalty of the aircraft stand waiting cost is as follows:
Figure GDA0003735126800000121
wherein β ═ ln (cG) max +1)]/G max C is the cost of fuel consumption per unit time during coasting, G max The maximum allowable waiting time for the stand;
in step 4), the expression of the derived frequency control model is as follows:
Figure GDA0003735126800000131
wherein C is T M is the total aircraft departure cost, wherein M is the total number of the aircraft requested to be released, and j is the index of the aircraft leaving the port; w is the taxiway queue waiting time, E [ W ] j ]Beta is a parking space waiting penalty coefficient for the expectation of the taxiway waiting time of the jth departure aircraft; g j For stand waiting time of jth departing aircraft, EG j ]Expectation of stand waiting time for the jth departure aircraft;
in step 6), the deducing a frequency control expression comprises:
the actual derived frequency:
Figure GDA0003735126800000132
service rate: mu.s
Reiterating the time interval: t is t r
Where λ' is the actual derived frequency; lambda is the frequency of application; n is the current taxiway queuing value; n is a taxiway queuing length threshold, and N/N is taxiway queuing saturation;
recording the average departure time interval of the aircraft, namely the service time as t t When the ratio of the repeat request time interval to the average departure time interval of the aircraft is given as g, g is t r /t t For the convenience of the following calculation, the reciprocal of the g value is recorded as h 1/g; the method for selecting the repeat request time interval is given as g-1, g>1 or g<1.
The method for selecting the reiteration time interval includes establishing a state transition equation set when g is 1, wherein for the taxiway queue, the established state transition equation set includes:
λπ 0 ＝μπ 1 (1)
λπ M-1 ＝μπ M (2)
Figure GDA0003735126800000133
Figure GDA0003735126800000134
wherein pi i I is the probability when the system is in state i, i is 0,1,2,3, ·, N;
at this time, the arbitrary state pi i Can be written as to 0 Is represented by the regular equation:
Figure GDA0003735126800000141
obtaining:
Figure GDA0003735126800000142
wherein
Figure GDA0003735126800000143
According to the calculation method of the length of the queue and the stay time of the queuing system, the expectation of the value of the length of the taxiway queue is as follows:
Figure GDA0003735126800000144
wherein:
Figure GDA0003735126800000145
Figure GDA0003735126800000146
the effective push-out rate is expected to be:
Figure GDA0003735126800000147
thus, the taxiway latency expectations are:
Figure GDA0003735126800000148
when the computer stands by the state, include:
A. when n is more than or equal to 0 and less than or equal to M, applying for the aircraft to be deduced with 1 probability, and then E [ G | k ═ n ] ═ 0;
B. when M is more than N and less than or equal to N, recording C aj For the number of times the jth aircraft in the stand queue applies,
for the 1 st aircraft, there is a state transfer function:
Figure GDA0003735126800000149
Figure GDA00037351268000001410
…
Figure GDA0003735126800000151
obtaining the waiting and repeat request times of the 1 st aircraft stand according to the relation between the state and the state probability,
the stand waiting time expectation is as follows:
Figure GDA0003735126800000152
for the 2 nd aircraft, the waiting time of the stand is expected to be related to the application times of the 1 st aircraft, and the waiting time is as follows:
Figure GDA0003735126800000153
③ further, for the n-th G An airborne vehicle with stand-off latency expectations of:
Figure GDA0003735126800000154
then the stand wait time for any one aircraft is expected to be:
Figure GDA0003735126800000155
when g is greater than 1, a state transition equation set is established, and the equations in the state transition equation set comprise:
note C b1 Obtaining C for the number of repeat requests of the 1 st aircraft in the stand waiting queue b1 The probability of (c) is:
Figure GDA0003735126800000156
Figure GDA0003735126800000157
Figure GDA0003735126800000158
…
Figure GDA0003735126800000159
when the taxiway queue length n is equal to 0, the first aircraft in the stand waiting queue enters the taxiway with the probability of 1, and then the first aircraft has
Figure GDA0003735126800000161
Obtaining the stand waiting time expectation E [ C ] of the 1 st aircraft by a probability transfer equation b1 ]The expression of (a) is:
Figure GDA0003735126800000162
due to the fact that
Figure GDA0003735126800000163
As the g value changes, the 2 nd aircraft may no longer be able to t t When the application is deduced at integral multiple of the time, the pair E [ C ] is b1 ]Is corrected, to
Figure GDA0003735126800000164
Comprises the following steps:
Figure GDA0003735126800000165
Figure GDA0003735126800000166
wherein
Figure GDA0003735126800000167
For the 2 nd and m nd aircraft, there are:
Figure GDA0003735126800000168
Figure GDA0003735126800000169
for stand waiting teamThe mth aircraft in the train, applying for the total number of times expected to be E [ C ] am ]＝E[C bm ]+ m, containing the initial application, assuming the initial application obeys [0, t ] r ]Uniformly distributed, then the stand wait time is expected to be
Figure GDA00037351268000001610
Said method of selecting a reiterated time interval is given as g<1, and
Figure GDA00037351268000001611
when the number of repeat requests is recorded as k, the quotient of k/h is recorded as u k The remainder v k For the 1 st aircraft in the stand waiting queue, the following transition probability state equation exists:
when k is 1, u k ＝0，v k 1, then there are:
Figure GDA00037351268000001612
when k is equal to 2, the number of the bits is increased,
Figure GDA00037351268000001613
the probability expression for restitution times k is:
Figure GDA0003735126800000171
solving a transition probability state equation, and obtaining the following information for the 1 st aircraft in the stand queue:
Figure GDA0003735126800000172
by
Figure GDA0003735126800000173
Property of (1), record
Figure GDA0003735126800000174
Quotient u of m The remainder v m The derivation process is the same as the derivation process of the 1 st aircraft, then
Figure GDA0003735126800000175
Preamble aircraft
Figure GDA0003735126800000176
The conditional probability expression of (a) is:
Figure GDA0003735126800000177
because it is difficult to directly calculate the residual conditional probability expression, a recursive unified algorithm is adopted, and the recursive unified algorithm comprises the following steps of converting the conditional probability of the next sequence into the expression related to the previous sequence:
for the 2 nd aircraft in the stand waiting queue, the stand waiting repeat request times are as follows:
Figure GDA0003735126800000178
for the mth aircraft in the stand waiting queue, there are:
Figure GDA0003735126800000181
and
Figure GDA0003735126800000182
establishing a state transition equation system, wherein the equations in the state transition equation system comprise:
for the mth aircraft in the stand waiting queue, the total number of applications for push-out is expected to be E [ C ] am ]＝E[C bm ]+ m, containing the initial application, assuming the initial application obeys [0, t ] r ]Is uniformly distributed, thenThe stand wait time is expected to be:
Figure GDA0003735126800000183
said method of selecting a reiterated time interval is given as g<1, and
Figure GDA0003735126800000184
when k is the number of repeated requests,
Figure GDA0003735126800000185
The quotient k/d is u k The remainder v k For the 1 st aircraft in the stand waiting queue, the probability expression that the number of reassessment times is k is as follows:
Figure GDA0003735126800000186
wherein
Figure GDA0003735126800000187
The number of times the aircraft stands waiting for reiteration for this aircraft is expected to be:
Figure GDA0003735126800000191
derived from the conditional probabilities of the preceding aircraft:
Figure GDA0003735126800000192
derived by a recursive unified algorithm:
Figure GDA0003735126800000193
Figure GDA0003735126800000194
converting the expression into the conditional probability relation between the 2 nd aircraft and any aircraft and the 1 st aircraft in the stand waiting queue:
Figure GDA0003735126800000201
and
Figure GDA0003735126800000202
for the mth aircraft in the stand waiting queue, the total number of applications for push-out is expected to be E [ C ] am ]＝E[C bm ]+ m, containing the initial application, assuming the initial application obeys [0, t ] r ]If so, the stand wait time is expected to be:
Figure GDA0003735126800000203
in step 6), the solving of the derived frequency control model in a loop iterative search manner includes the following steps, as shown in fig. 1:
6-1) inputting a data set of a planned application release time of an aircraft s;
6-2) inputting a reapplication push-out interval time;
6-3) judging that g belongs to the type of g ═ 1, g >1 and g < 1;
6-4) sequencing all the aircraft push-out sequences according to the ascending sequence of application time;
6-5) initializing taxiway queue length threshold N for aircraft s s ；
6-6) the aircraft j applies for release from the tower, and marks the time when the aircraft j applies for release;
6-7) judging whether the current taxiway queuing length n when the aircraft j applies for release meets n<N s If yes, continuing; if not, marking the aircraftThe state of j is stand waiting and the waiting time G of the current aircraft j at the stand is judged i If the number of taxiways is larger than the preset value, updating the taxiway queuing length threshold value to be N s +1, over t r After the time period, repeating the application and release of the aircraft j to the tower, marking the application and release time of the aircraft j and judging whether the current taxiway queuing length n of the aircraft j meets n<N s + 1; if not, judging whether the derived applied aircraft index j of the aircraft j meets j or not<M, wherein M represents the maximum value of the aircraft index requested to be released, if yes, the aircraft index requested to be released is updated to be j +1, the aircraft j +1 applies to be released to a tower, the time when the aircraft j +1 applies to be released is marked, and if not, the taxiway fuel cost, the stand waiting penalty cost and the total cost release value C of the aircraft j are calculated Tj ；
6-8) triggering a probability simulation mechanism to judge the random number R j Whether E (0,1) satisfies R j <(1-n/N s ) If so, agreeing to the release application of the aircraft j, marking the position of the aircraft j as a taxiway queue, recording the taxiway waiting time of the aircraft j, and continuing; if not, marking the state of the aircraft j as the stand waiting and judging the waiting time G of the current aircraft j at the stand i If the number of taxiways is larger than the preset value, updating the taxiway queuing length threshold value to be N s +1, repeating the steps of applying for release from the tower by the aircraft j and marking the time of applying for release, and judging whether the taxiway queuing length n of the aircraft j meets n<N s +1；
6-9) judging whether the pushing of all the aircrafts in the time window is finished or not, including judging whether the pushing application aircraft index j of the aircraft j meets j or not<M, wherein M represents the maximum value of the pushed application aircraft index, if yes, the pushed application aircraft index is updated to be j +1, the aircraft j +1 is pushed to a tower to mark the pushing time of the aircraft j +1, and if not, the taxiway fuel cost, the stand waiting penalty cost and the pushed total cost value C of the aircraft j are calculated Tj ；
6-10) judgmentTaxiway queuing length threshold N of aircraft-breaking j s Whether or not N is satisfied s <N max Wherein N is max A maximum value representing a taxiway queue length threshold; if yes, updating the taxiway queuing length threshold to be N s + 1; if not, continuing;
6-11) calculating N s Corresponding to the sum C of the derived total cost values Ts Comparing all of said calculated extrapolated total cost values C Ts Outputting the minimum deducing total cost value C Ts ；
6-12) updating the release repeat request time interval, jumping to the step 6-3), and judging the ratio g of the release repeat request time interval to the service time interval k Whether or not g is satisfied k <g max If yes, continuing; if not, calculating the current g value to push out the optimal total cost value C Tg ；
6-13) comparing all said calculated extrapolated total cost values C Tg Outputting the minimum deducing total cost value C T * As an optimal extrapolated total cost value.
The pushed frequency control expression is obtained by obtaining a corresponding taxiway queuing length threshold value, an average parking space waiting time, an average taxiway sliding time and an optimal pushed re-application time interval according to an optimal pushed total cost value, and substituting the optimal pushed total cost value, the corresponding taxiway queuing length threshold value, the average parking space waiting time, the average taxiway sliding time and the pushed re-application time interval into the pushed frequency control model.
The method for controlling the waiting and pushing-out of the aircraft stand with the controllable repeat request time interval provided by the invention is specifically described below by combining specific scenes.
Step 1: the method comprises the steps of preprocessing acquired departure data of a certain large hub airport in China, leaving few flight time periods, only reserving flight data of 6: 00-22: 00, converting planned push-out time into a minute format, setting 6:00 as a base point 0, converting 6:00 into 0, and converting 8:00 into 120, so that the control effect of the method provided by the invention is more prominent;
and 2, step: selecting an average departure time interval of 1.7 minutes; the fuel cost is calculated by 125 yuan per minute of sliding cost; penalty factor is based on β ═ ln (cG) max +1)]/G max Calculation, β — 0.2743; adopting a push-out frequency control model:
Figure GDA0003735126800000221
and step 3: the step of carrying out optimization solution on the model by adopting the continuous time Markov chain-based iterative optimization algorithm provided by the embodiment of the disclosure obtains the optimal departure total cost, the optimal taxiway queuing length threshold, the optimal reapplication release time interval, the average taxiway waiting time and the average stand waiting time.
According to different busy degrees of hub airports and different service times, the inventor compares the waiting push-out control effect of aircraft stands with controllable reapplication time intervals and the control effect of no control and traditional N-control under different service time conditions, and the comparison result is shown in Table 1:
TABLE 1
Figure GDA0003735126800000222
In Table 1, t t G is the ratio of the repeat request time interval to the average departure time, C T To derive a total cost value, N is a taxiway queue length threshold, G is the mean wait time for the stand, w is the mean wait time for the taxiway, C T(N-control) Optimum departure cost for N-control method under the same conditions, C T(No-control) The departure cost is the cost under the same condition without control. Gap1 and Gap2 are the percentage reduction in the calculated cost of the present invention and the cost of the other methods, respectively. Wherein except t t When the control effect is equal to the N-control effect in 1 minute, the control effect of the invention is better than the control effect of the non-control and the N-fentrol control effect in other situations, and the description shows thatThe departure cost can be effectively reduced.
In summary, in the method for controlling waiting for release of an aircraft stand with a controllable repeat request time interval provided in the embodiment of the present disclosure, the method includes: according to the departure operation characteristics of the aircraft, proposing the assumed conditions of modeling the departure control process of the aircraft; the aircraft departure operation characteristics comprise weather, queuing forms, takeoff intervals and the like; establishing an aircraft push-out frequency control rule, wherein the control rule comprises the linear decline of push-out frequency along with the increase of taxiway queuing saturation, and the taxiway queuing saturation is the ratio of the current taxiway queuing length value to the taxiway queuing length threshold; determining a punishment rule of the waiting cost of the aircraft stand according to the maximum waiting time of the stand of the aircraft allowed in the airport and the fuel consumption cost of the aircraft in the unit time in the process of sliding; establishing a derived frequency control model according to the stand waiting penalty cost and the fuel consumption cost; abstracting the pushing process into a retrying M/M/1/K queuing process with a variable input rate, wherein the states in the queuing process comprise a stand waiting state and a taxiway queuing state, and respectively calculating the expectation of the key index stand waiting time of the stand waiting state, the expectation of the key index taxiway waiting time of the taxiway queuing state, the expectation of the effective pushing rate and the expectation of the pushing restitution time interval; solving the push-out frequency control model in a cyclic iterative search mode by combining the expectation of the stand waiting time, the expectation of the taxiway waiting time, the expectation of the effective push-out rate and the expectation of the push-out restitution time interval to obtain an optimal push-out frequency control expression, and controlling the push-out frequency of the aircraft according to the optimal push-out frequency control expression;
furthermore, the push-out frequency control model is solved by using an iterative optimization algorithm based on a continuous time Markov chain, so that an airport is helped to find an optimal annual threshold value of the queuing length of the sliding way and an optimal reapplication push-out time interval of the control method, and airport dispatchers are helped to make a high-efficiency push-out control decision.

Claims (8)

1. An aircraft stand-by pushout control method with a controllable repeat request time interval, characterized by comprising the steps of:
1) according to the departure operation characteristics of the aircraft, proposing an assumed condition of modeling the departure control process of the aircraft; the aircraft departure operation characteristics comprise weather, queuing forms and takeoff interval characteristics;
2) establishing an aircraft push-out frequency control rule which linearly decreases along with the increase of the taxiway queuing saturation, wherein the taxiway queuing saturation is the ratio of the current taxiway queuing length value to the taxiway queuing length threshold value;
3) determining a punishment rule of the waiting cost of the aircraft stand according to the maximum waiting time of the stand of the aircraft allowed in the airport and the fuel consumption cost of the aircraft in the unit time in the process of sliding;
4) establishing a derived frequency control model according to the fuel consumption cost and the waiting cost of the aircraft parking space;
5) abstracting the push-out process of the push-out frequency control model into a retry M/M/1/K queuing process with variable input rate, wherein the state in the queuing process comprises the following steps: respectively calculating the expectation of the key index of the stand waiting state, the expectation of the key index of the taxiway queuing state, the expectation of the key index of the taxiway waiting time, the expectation of the effective push-out rate and the expectation of the push-out request time interval;
6) solving the push-out frequency control model in a cyclic iterative search mode by combining the expectation of the stand waiting time, the expectation of the taxiway waiting time, the expectation of the effective push-out rate and the expectation of the push-out restitution time interval to obtain an optimal push-out frequency control expression, and controlling the push-out frequency of the aircraft according to the optimal push-out frequency control expression;
in step 3), the determining method of the aircraft stand waiting cost penalty rule is to select an exponential function to represent the penalty of the aircraft stand waiting cost, and the expression of the penalty of the aircraft stand waiting cost is as follows:
Figure FDA0003735126790000011
whereinβ＝[ln(cG max +1)]/G max C is the cost of fuel consumption per unit time during coasting, G max The maximum value of the allowed waiting time of the stand is set;
in step 4), the expression of the derived frequency control model is as follows:
Figure FDA0003735126790000012
wherein C is T For the total cost of aircraft departure, M is the total number of aircraft requested, j is the departure aircraft index, E [ W ] j ]Beta is an expectation of taxiway waiting time of the jth departure aircraft, and is a stand waiting penalty coefficient; g j For stand waiting time of jth departing aircraft, EG j ]Expectation of stand waiting time for the jth departure aircraft;
in step 6), the deducing a frequency control expression comprises:
the actual derived frequency:
Figure FDA0003735126790000021
service rate: mu.s
Push-repeat interval: t is t r
Where λ' is the actual derived frequency; lambda is the frequency of application; n is the current taxiway queuing value; n is a taxiway queuing length threshold, and N/N is the taxiway queuing saturation;
recording the average departure time interval of the aircraft, namely the service time as t t When the ratio of the repeat request time interval to the average departure time interval of the aircraft is given as g, g is t r /t t Recording the reciprocal of the g value as h 1/g; the method for selecting the repeat request time interval is given as g-1, g>1 or g<1.
2. The method of claim 1, wherein the method for selecting the reiteration time interval establishes a set of state transition equations when g is 1, wherein the set of state transition equations comprises, for a taxiway queue:
λπ 0 ＝μπ 1 (1)
λπ M-1 ＝μπ M (2)
Figure FDA0003735126790000022
Figure FDA0003735126790000023
wherein pi i I is the probability when the system is in state i, i ═ 0,1,2,3, ·, N;
at this time, the arbitrary state pi i Can be written as to 0 Is represented by the regular equation:
Figure FDA0003735126790000024
obtaining:
Figure FDA0003735126790000025
wherein
Figure FDA0003735126790000026
According to the calculation method of the length of the queue and the stay time of the queuing system, the expectation of the value of the length of the taxiway queue is as follows:
Figure FDA0003735126790000031
wherein:
Figure FDA0003735126790000032
Figure FDA0003735126790000033
the effective push-out rate is expected to be:
Figure FDA0003735126790000034
thus, the taxiway latency expectations are:
Figure FDA0003735126790000035
when the computer stands by the state, include:
A. when n is more than or equal to 0 and less than or equal to M, the application aircraft deduces with 1 probability that E [ G | k ═ n ] ═ 0;
B. when M is more than N and less than or equal to N, recording C aj For the number of times the jth aircraft in the stand queue applies,
for the 1 st aircraft, there is a state transfer function:
Figure FDA0003735126790000036
Figure FDA0003735126790000037
…
Figure FDA0003735126790000038
according to the relation between the state and the state probability, obtaining the waiting and re-applying times of the 1 st aircraft stand, wherein the stand waiting time expectation is as follows:
Figure FDA0003735126790000039
secondly, for the 2 nd aircraft, the expectation of the stand waiting time of the aircraft is related to the expectation of the number of times of application of the 1 st aircraft, and the expectation is as follows:
Figure FDA0003735126790000041
③ further, for the n-th G An airborne vehicle with a stand wait time desired to be:
Figure FDA0003735126790000042
the stand wait time for any one aircraft is expected to be:
Figure FDA0003735126790000043
3. the method of claim 1, wherein the method for selecting the reiteration-related time interval is used to establish a set of state transition equations when g >1, the equations in the set of state transition equations including:
note C b1 The number of repeat requests of the 1 st aircraft in the queue is waited for the parking space, C is obtained b1 The probability of (c) is:
Figure FDA0003735126790000044
Figure FDA0003735126790000045
Figure FDA0003735126790000046
…
Figure FDA0003735126790000047
when the taxiway queuing length n is 0, the first aircraft in the stand waiting queue enters the taxiway with the probability of 1, and then the first aircraft in the stand waiting queue enters the taxiway
Figure FDA0003735126790000048
Obtaining the stand waiting time expectation E [ C ] of the 1 st aircraft by a probability transfer equation b1 ]The expression of (a) is:
Figure FDA0003735126790000049
due to the fact that
Figure FDA0003735126790000051
As the g value changes, the 2 nd aircraft may not be able to operate at t t When the application is deduced at integral multiple of the time, the pair E [ C ] is b1 ]Is corrected, to
Figure FDA0003735126790000052
Comprises the following steps:
Figure FDA0003735126790000053
wherein
Figure FDA0003735126790000054
For the 2 nd and m nd aircraft, there are:
Figure FDA0003735126790000055
Figure FDA0003735126790000056
for the mth aircraft in the stand waiting queue, the total number of applications for push-out is expected to be E [ C ] am ]＝E[C bm ]+ m, containing the initial application, assuming the initial application obeys [0, t ] r ]With even distribution of the above, the stand wait time is expected to be
Figure FDA0003735126790000057
4. The method of claim 1, wherein the reiteration time interval is selected as g<1, and
Figure FDA0003735126790000058
when the number of repeat requests is recorded as k, the quotient of k/h is recorded as u k Remainder is v k For the 1 st aircraft in the stand waiting queue, the following transition probability state equation exists:
when k is 1, u k ＝0，v k 1, then there are:
Figure FDA0003735126790000059
when the k is equal to 2, the reaction condition is as follows,
Figure FDA00037351267900000510
the probability expression for restitution times k is:
Figure FDA00037351267900000511
solving a transition probability state equation, and obtaining expectation of the number of times of waiting for repeat application of the aircraft stand of the aircraft for the 1 st aircraft in the stand queue:
Figure FDA0003735126790000061
by
Figure FDA0003735126790000062
Property of (1), record
Figure FDA0003735126790000063
Quotient of u m Remainder is v m The derivation process is the same as the derivation process of the 1 st aircraft, then
Figure FDA0003735126790000064
Preamble aircraft
Figure FDA0003735126790000065
The conditional probability expression of (a) is:
Figure FDA0003735126790000066
because it is difficult to directly calculate the residual conditional probability expression, a recursive unified algorithm is adopted, and the recursive unified algorithm comprises the following steps of converting the conditional probability of the next sequence into the expression related to the previous sequence:
for the 2 nd aircraft in the stand waiting queue, the stand waiting repeat request times are as follows:
Figure FDA0003735126790000067
for the mth aircraft in the stand waiting queue, there are:
Figure FDA0003735126790000071
and
Figure FDA0003735126790000072
establishing a state transition equation set, wherein equations in the state transition equation set include:
for the mth aircraft in the stand waiting queue, the total number of applications for push-out is expected to be E [ C ] am ]＝E[C bm ]+ m, containing the initial application, assuming the initial application obeys [0, t ] r ]Then the stand wait time is expected to be:
Figure FDA0003735126790000073
5. the method as claimed in claim 1, wherein the reiteration time interval is selected as g<1, and
Figure FDA0003735126790000074
when k is the number of repeated requests,
Figure FDA0003735126790000075
The quotient k/d is u k The remainder v k； Note book
Figure FDA0003735126790000076
Quotient of u m Remainder is v m (ii) a For the 1 st aircraft in the stand waiting queue, the probability expression that the number of reassessment times is k is as follows:
Figure FDA0003735126790000077
wherein
Figure FDA0003735126790000078
The number of times the aircraft stands waiting for reiteration for this aircraft is expected to be:
Figure FDA0003735126790000081
derived from the conditional probabilities of the preamble aircraft:
Figure FDA0003735126790000082
derived from a recursive unified algorithm:
Figure FDA0003735126790000083
Figure FDA0003735126790000084
converting the expression into the conditional probability relation between the 2 nd aircraft and any aircraft and the 1 st aircraft in the stand waiting queue:
Figure FDA0003735126790000091
and
Figure FDA0003735126790000092
for stand waitingThe mth aircraft in the queue, applying for a total number of pushout expectations E [ C ] am ]＝E[C bm ]+ m, containing the initial application, assuming the initial application obeys [0, t ] r ]Then the stand wait time is expected to be:
Figure FDA0003735126790000093
6. the method for controlling the hold-off waiting release of aircraft stands with controllable repeat request time interval according to claim 1, wherein in step 6), the solution of the release frequency control model in a cyclic iterative search manner comprises the following steps:
6-1) inputting a data set of a planned application release time of an aircraft s;
6-2) inputting a reapplication push-out interval time;
6-3) judging that g belongs to the type of g ═ 1, g >1 and g < 1;
6-4) sequencing all the aircraft push-out sequences according to the ascending sequence of application time;
6-5) initializing taxiway queue length threshold N for aircraft s s ；
6-6) the aircraft j applies for release from the tower, and marks the time when the aircraft j applies for release;
6-7) judging whether the current taxiway queuing length n when the aircraft j applies for release meets n<N s If yes, continuing; if not, marking the state of the aircraft j as stand waiting and judging the waiting time G of the current aircraft j at the stand i If the number of taxiways is larger than the preset value, updating the taxiway queuing length threshold value to be N s +1, over t r After the time period, repeating the application and release of the aircraft j to the tower, marking the application and release time of the aircraft j and judging whether the current taxiway queuing length n of the aircraft j meets n<N s + 1; if not, judging whether the pushed application aircraft index j of the aircraft j meets j or not<M, wherein M represents the application pushoutIf the maximum value of the aircraft index is positive, updating and deducing the application aircraft index to be j +1, applying and deducing the aircraft j +1 to a tower, marking the time when the aircraft j +1 applies for deduction, and if the maximum value of the aircraft index is negative, calculating the taxiway fuel cost, the stand waiting penalty cost and the deducing total cost value C of the aircraft j Tj ；
6-8) triggering a probability simulation mechanism to judge the random number R j Whether E (0,1) satisfies R j <(1-n/N s ) If so, agreeing to the release application of the aircraft j, marking the position of the aircraft j as a taxiway queue, recording the taxiway waiting time of the aircraft j, and continuing; if not, marking the state of the aircraft j as stand waiting and judging the waiting time G of the current aircraft j at the stand i If the number of taxiways is larger than the preset value, updating the taxiway queuing length threshold value to be N s +1, repeating the steps of applying for release from the tower by the aircraft j and marking the time of applying for release, and judging whether the taxiway queuing length n of the aircraft j meets n<N s +1；
6-9) judging whether the pushing of all the aircrafts in the time window is finished or not, including judging whether the pushing application aircraft index j of the aircraft j meets j or not<M, wherein M represents the maximum value of the pushed application aircraft index, if yes, the pushed application aircraft index is updated to be j +1, the aircraft j +1 applies for pushing to a tower, the time when the aircraft j +1 applies for pushing is marked, and if not, the taxiway fuel cost, the stand waiting penalty cost and the pushed total cost value C of the aircraft j are calculated Tj ；
6-10) determining a taxiway queuing length threshold N for aircraft j s Whether or not N is satisfied s <N max Wherein N is max A maximum value representing a taxiway queue length threshold; if yes, updating the taxiway queuing length threshold to be N s + 1; if not, continuing;
6-11) calculating N s Corresponding to the sum C of the derived total cost values Ts Comparing all of said calculated extrapolated total cost values C Ts Outputting the minimum deducing total cost value C Ts ；
6-12) updating the release repeat request time interval, jumping to the step 6-3), and judging the ratio g of the release repeat request time interval to the service time interval k Whether or not g is satisfied k <g max If yes, continuing; if not, calculating the current g value to push down the optimal total cost value C Tg ；
6-13) comparing all of said calculated extrapolated total cost values C Tg Outputting the minimum deducing total cost value C T * As an optimal extrapolated total cost value.
7. The method as claimed in claim 1, wherein the derived frequency control expression is obtained by substituting the optimal derived total cost value and the corresponding taxiway queuing length threshold, the average parking space waiting time, the average taxiway taxi time and the optimal derived restitution time interval into the derived frequency control model according to the optimal derived total cost value, the average taxiway queuing length threshold, the average parking space waiting time and the average derived restitution time interval.
8. The method for controlling the push-out waiting of the aircraft stand with the controllable restitution time interval as claimed in claim 1, wherein in the step 1), the departure operation characteristics of the aircraft refer to preprocessing the acquired airport departure data and converting the format of the acquired data set at the push-out time of the planned application into a minute system; the assumed conditions for modeling the aircraft launch control process comprise: ignoring the influence of meteorological conditions, the launch phase accomplished by the tow vehicle does not consume fuel, which consumes no time to account for the taxi time of the aircraft, which is subject to first come first serve rules.
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