WO1994011972A1

WO1994011972A1 - A method and apparatus for estimating traffic in an asynchronous telecommunications network

Info

Publication number: WO1994011972A1
Application number: PCT/AU1993/000583
Authority: WO
Inventors: Sammy Chi Hung Chan; Robert Edwin Warfield
Original assignee: Telstra Corporation Limited
Priority date: 1992-11-13
Filing date: 1993-11-12
Publication date: 1994-05-26

Abstract

A method and apparatus for estimating traffic in an asynchronous telecommunications network, which can provide estimates in real-time and can be adapted to suit the speed of variations in the cell traffic. Synchronous iterative loops accumulate detected cell arrivals and inter-arrival times, with the accumulation of previous values being modified by a response factor. A ratio of the outputs from the synchronous loops can be calculated asynchronously to provide an estimate of cell traffic. The output from two estimators utilising different response factors can be latched according to detected changes in cell traffic so as to provide either a smooth but accurate response, responding slowly to variations in traffic, or a fast but noisy response.

Description

A METHOD AND APPARATUS FOR ESTIMATING TRAFFIC IN AN ASYNCHRONOUS TELECOMMUNICATIONS NETWORK

This invention relates to the estimation of traffic in an asynchronous telecommunications network.

In telecommunications systems, network utilisation in an important consideration, particularly where optimal use is to be made of network resources. Ideally the network is utilised to the greatest extent possible without introducing congestion at the network nodes or in the network links. In order to avoid congestion it is necessary for a network controller to be able to control telecommunications traffic arriving at a node or passing through a link, so as to reduce traffic arrivals when the onset of congestion appears likely. For the network controller to be effective it may be necessary for the controller to have knowledge of the actual rate of telecommunication traffic arrivals at the node. In asynchronous digital networks, such as an Asynchronous Transfer Mode (ATM) network, traffic arrivals may be a stochastic process, and hence traffic rates may not be readily calculated on a real time basis.

An Asynchronous Transfer Mode (ATM) network is a connection-oriented high- speed packet switching network. Information is carried using small (48 octets of user data plus 5 octets of header) fixed length packets, called cells. These cells are transmitted across the network via a series of node-to-node links, which are collectively called a path. Each link in the path carries an aggregate cell stream multiplexed from a number of connections. Multiplexing is performed asynchronously: cells are queued and interleaved onto the links without reference to any fixed multiplexing structure (such as Time Division Multiplexing). Asynchronous multiplexing is fast, but means that traffic from one customer may well interfere with the traffic from another.

Based on the Asynchronous Transfer Mode (ATM), it is possible to perform statistical multiplexing of bursty and variable bit rate traffic to achieve a higher bandwidth utilisation in Broadband Integrated Systems Digital Networks (B-ISDN). This gain in utilisation, however, comes at the risk of congestion and hence degraded Quality of Service QoS, when too many sources transmit simultaneously at their peak rates and the sum of which exceeds the bandwidth of the outgoing link. Therefore, some traffic controls are necessary to ensure that satisfactory QoSs are delivered to users, and at the same time, a reasonably high bandwidth utilisation is achieved.

Briefly, the Quality of Service (QoS) is the means of defining the expected performance of the ATM network, as seen by a customer. Any true measure of the QoS must cover all aspects of the customer's perception of the service. With ATM networks, the primary QoS parameters are the cell loss ratio (i.e. the ratio of cells discarded due to network congestion), the end-to-end cell transfer delay (i.e. the average time it takes to transmit a cell through the network), and the cell delay variation. Some other QoS parameters are the ratio of connection requests blocked due to insufficient network resources, the ratio of cells corrupted while passing through the network, and the connection establishment and connection release delays.

At the time of connection request the customer must supply to the service provider information that characterises the expected traffic flow, and the required QoS. A decision on whether the network can support this connection is then made. If not, the QoS and/or other traffic parameters may be re-negotiated, or the connection rejected out-right. The act of determining whether a new connection can be admitted to the network without causing congestion is called Connection Admission Control (CAC).

The B-ISDN is an integrated network able to carry normal telephony, video- telephony, high-resolution video-conferencing, data (e.g. LAN traffic) and high-quality imaging; plus any other services as they appear. The expected traffic from these sources varies widely. If the network cost per connection is to be minimised, utilisation must be as high as possible without incurring excessive control costs. If B-ISDN connection admission were based on a single call class, as in the Public Switched Telephone Network (PSTN), gross under-utilisation of the network would result. Similarly, the logical channel approach of the Packet Switched Public Data Network (PSPDN) is also inadequate. Therefore, in the B-ISDN, the calling party is required to supply a series of traffic parameters which define its expected traffic profile. Knowing the current state of the network, the CAC can then predict the impact of the new connection, and decide according. Thus, the emphasis is not on actual calls, but the expected aggregate traffic.

Connection Admission Control is only one of a number of Traffic Control and Resource Management techniques. Collectively these techniques regulate access to network resources so that acceptable Quality of Service is provided to all customers. A brief description of some of these techniques follows:

Usage Parameter Control: Once a connection has been admitted to the network the traffic from that connection must be monitored to ensure that the customer-supplied traffic parameters are not violated. This maintains the integrity of the CAC decision.

Congestion Control: If both the Usage Parameter and the Connection Admission Controls are functioning correctly, network congestion should be rare, but not eliminated. Congestion Controls define how the network should react to congestion so that this is speedily remedied.

Resource Management: How the network routes connections and the allocation of capacity to virtual path connections have a marked effect on the likelihood of network congestion. Resource Management aims to reduce congestion by proper dimensioning of the network.

Proper Control: The ATM protocol allows the customer to generate cells at two priority levels (either explicitly or implicitly). During congestion periods low-priority cells may be discarded to maintain the QoS of the high-priority cells.

Generally, the traffic control framework for B-ISDN consists of control actions at both call and cell level. When there is a call request, the connection acceptance control (CAC), which is the call level control, decides whether to accept or reject the request by considering the current network loading and the traffic parameters declared for the new call. The request is accepted only if the desired QoS of the new call can be guaranteed without affecting the QoSs of those already established connections. Once a call is accepted, its traffic parameters are monitored by the usage parameter control (UPC), which is the cell level control. When UPC detects violating cells, it either discards them immediately or puts a tag in the cell header but still admits them into the network. The tagged cells are then discarded only when and if they reach a congested node.

So far, most of the traffic control algorithms discussed in the literature are open loop. They aim to avoid congestion by controlling traffic sources at the network entry without taking into account the actual loading condition of the network. Some CAC algorithms, for example, assume that the network load is always equivalent to the sum of load declared by the existing connections. However, reactive controls may also be necessary to reduce the severity of potential congestion events and improve the network's ability to recover from a congested state. These reactive controls may include adaptive CAC, adaptive UPC, explicit congestion notification and feedback flow control. All of these control functions rely on some information on the loading condition within the network. Some typical parameters that reflect the traffic condition are cell arrival rate, link utilisation and buffer occupancy. Since these parameters are stochastic, the measured data in the network is only one sample realisation of the underlying stochastic process, and thus cannot be used directly by reactive controls. Instead, they may be used by an estimation algorithm such as that described hereinafter as input data to estimate the actual parameters.

The problem of estimating these parameters based on measured data is essentially a filtering problem frequently encountered in other areas such as signal processing and control engineering. In this case, the measured data is like a noisy signal and the problem is how to extract the signal from noise. This problem has been studied, and generally the methods proposed involve calculating covariance functions of the measured data and then solving systems of equations. This computational process is repeated every time an estimation is made because the parameters may be time varying. Since ATM networks operate in such high speed, estimations need to be made in real-time making these methods computationally unfeasible. In one paper (H. Ahmadi and P. Kermani,

"Real Time Network Load Estimation in Packet Switched Networks", Proc. of IFIP, pp.

367-380,1992) an heuristic estimation algorithm is proposed which consists essentially of a simple averaging filter and an exponential smoothing filter. Another estimation technique (presented in P.S. Khedkar and S. Keshav, "Fuzzy Prediction of Timeseries",

Proc. of FUZZ-IEEE'92, San Jose, March 1992 also uses exponential averaging filter, but with the weighting factor dynamically adjusted by a fuzzy logic controller.

In accordance with the present invention, there is provided a method for estimating telecommumcations traffic in an asynchronous digital telecommunications network comprising the recursive steps of:

upon arrival of a cell at a node, measuring an inter-arrival time t_i between the arrival of the cell and a previous cell;

determining an inter-arrival time parameter S_i+1 based on the sum of the measured inter-arrival time t_i and a previous value of the inter-arrival time parameter modified by a response factor;

determining an arrival register value m_i+1 by incrementing a previous value of the arrival register value modified by the response factor; and

estimating cell traffic on the basis of a ratio between the arrival register value and the inter-arrival time parameter.

The invention also provides an apparatus for estimating telecommunications traffic in an asynchronous digital telecommunications network comprising:

timing means to determine an inter-arrival time between cells;

an arrival register means for determining an arrival register value by incrementing a previous arrival register value as modified by a response factor;

an inter-arrival time register means for summing the inter-arrival time determined by the timing means with a previous inter-arrival time register value as modified by said response factor; and

estimating means for estimating cell traffic on the basis of a ratio between the arrival register value and the inter-arrival time register value.

Preferably, the value of the response speed parameter, which determines the value of the response factor, affects the speed at which the cell traffic estimate responds to changes in actual cell traffic in a real time recursive application of the method or apparatus. The response factor K is preferably in the range 0 to 1, and it calculated according to

K = (1 - 2^-n) where n is an integer value constituting said response speed parameter. Preferably an initial arrival register value estimate is added to the arrival register value and an initial inter-arrival time value estimate is added to the inter-arrival time register value, prior to the ratio thereof being determined for the purposes of estimating cell traffic. Preferably the cell traffic estimate is determined according to

where E is the estimate of cell traffic and m₀ and S₀ are estimated initial values for the arrival register value and inter-arrival time value respectively.

In one embodiment, first and second values of cell traffic are estimated by the method or apparatus described above using respective values of the response speed parameter such that the first traffic estimate is characterised by a relatively faster response time as compared to the second traffic estimate, and wherein a final traffic estimate is based on the first traffic estimate when rapid changes in traffic are detected and otherwise based on the second traffic estimate. In one embodiment rapid changes in traffic are detected by comparing the difference between the first traffic estimate and a previous value of the final traffic estimate with a threshold value.

Preferably, following a detected rapid change, the previous value for the interarrival time value and arrival register value in respect of the second traffic estimate are substituted with corresponding values constituting the first traffic estimate.

The invention is described in greater detail hereinafter, by way of example only, with reference to the accompanying drawings, in which:

Figure 1 is a diagrammatic representation of several forms of traffic sources in an Asynchronous Transfer Mode (ATM) network;

Figure 2 is a schematic representation of a first embodiment of the invention; Figure 3 is a schematic representation of a second embodiment of the invention;

Figures 4a to 4d illustrates some simulation results utilising the first embodiment of the invention; and

Figures 5a(i) and 5b(i) illustrate some further simulation results utilising the first embodiment, whilst Figures 5a(ii) and 5b(ii) illustrate some simulation results utilising the second embodiment of the invention.

The need for a real time estimator for traffic arrival rates in a network link or node is discussed above, and is brought about primarily because traffic parameters declared by a traffic source are not always indicative of the arrival rate of traffic from that source. Further, depending upon the particular traffic source, and the way in which different sources are multiplexed on the network, the traffic arrival rate may be a stochastic process which may only be characterised by statistical functions.

Presently, the type of traffic control and resource management actions implemented in B-ISDN are determined in part by the characteristics of the offered traffic and their quality of service requirements. Figure 1 illustrates a simple classification of ATM traffic sources as Continuous Bit Rate (CBR), sporadic (bursty) or Variable Bit Rate (BVR). An additional traffic source type referred to as negotiated stepwise Variable Bit Rate (VBR) is included to describe the aggregation of sporadic sources (this type of source may be an appropriate model for the traffic generated by a LAN interconnect service). Each arrow in Figure 1 corresponds to the instants at which the data units (cells) are transferred across the originating connection end-point.

In general, the parameters necessary to describe different sources are related to the multiplexing schemes used in the network. Possible multiplexing schemes for the traffic sources in Figure 1 are described below. CBR Sources

Constant Bit Rate (CBR) traffic sources require peak rate allocation for their duration to ensure that an appropriate quality of service is provided. The peak cell rate is sufficient to describe a CBR traffic source. Additionally, the network operator may require some indication of the anticipated holding time of a connection.

Bursty or Sporadic Sources

These sources are characterised by periods of activity during which information is sent at some rate (possibly fixed), followed by periods of inactivity during which no cells are sent. An appropriate multiplexing scheme for these sources may rely on various approaches for fast allocation of resources within the network. These fast allocation procedures attempt to allocate resources when bursts of information are transmitted and release these resources as soon as bursts end. By doing this, the network CAC mechanism does not have to allocate resources to the connection immediately following establishment.

A characterisation of a bursty source may need to specify the peak cell rate during bursts, the maximum peak duration and the expected overall average rate for the connection.

Negotiated Stepwise VBR Sources

The bursty sources described above are a subset of this more general traffic source type. These sources are characterised by periods of different peak cell rate. Changes in the peak cell rate from one period to another are negotiated with the network, perhaps using a fast allocation scheme. An increase in peak cell rate is granted only if the network has sufficient spare resource to accommodate the new peak cell rate.

In establishing a connection for a negotiated stepwise VBR source, the network

CAC may consider the peak cell rate in the period of highest activity, the duration of the period of highest activity and the expected overall average rate for connection. As with the bursty sources described above, the network CAC mechanism does not have to allocate any resources to the connection immediately following establishment. VBR

A Variable Bit Rate (VBR) source (e.g. a VBR video codec) sends cells at a rate which varies depending on the amount of information to be sent. This source differs from the negotiated stepwise VBR source in that the change in the amount of information to be sent occurs in an interval which is less than the minimum achievable response time using fast allocation procedures. Hence it is not possible to renegotiate the network resource allocation during a connection of this type.

In this case, the network CAC must determine the acceptance of a connection based on the parameters provided at establishment. For some VBR sources, a multiplexing scheme based on minimum throughput allocation may be appropriate. This scheme assumes that there is a minimum useful throughput for a VBR source which should always be provided at the highest level of quality of service. Cells sent in excess of this minimum rate would be subject to a lower guarantee of service.

In order for this scheme to provide two levels of guaranteed service, a VBR source would need to specify the peak cell rate, the minimum required cell rate and also the anticipated average rate for the connection. If the average rate is not specified, the network has no knowledge of the extent to which users will transmit information in excess of the minimum rate and it would not be possible to provide a guaranteed service to these cells.

Connection admission control (CAC) schemes for each of these traffic types may all be improved if an indication of actual traffic arrival rates are available, in addition to projected traffic arrival rates. This is particularly true with respect to variable bit rate sources, which are essentially stochastic in nature, and cannot therefore be readily predicted other than statistically. The embodiments of the present invention recognise the stochastic nature of such sources, and provide means by which traffic arrival rates may be estimated in real time using relatively simple algorithms and apparatus. A derivation of algorithms utilised by the preferred embodiments is discussed in attached Appendix A and any equations referred to in the description hereinafter relates to the Appendix. Figure 2 shows a schematic representation of a traffic estimator 2 based on algorithms developed from relationships as derived in Appendix A. In particular, an estimate of traffic arrival rate E may be represented as E(λ |t_{1,..., m}) =

whilst the variance of traffic arrival rate may be represented as

where λ is representative of the traffic arrival rate and tj are measured inter-arrival times. Further, m_i+1 is an arrival register value which may be calculated by m_i+1 = (1 - 2^-n)m_i+1 and s_i+1 is an inter-arrival time parameter which may be calculated by S_i+1 = (1 - 2^-n)s_i+t ₁

The value of (1-2^-n) may be thought of as a response factor K, in which n is a response speed parameter which may be chosen to suit the needs of the estimator. The values S_o and m_o are found from

1

S_o = maximum - average m_o =

average _{- 1}

maximum - average wherein the "maximum" and "average" values are estimated maximum and average traffic arrival rates for the applicable traffic stream or streams, and may, for example, be estimated from the parameters supplied by the traffic sources.

Referring to the block diagram of the traffic estimator (2) shown in Figure 2, there is shown a synchronous portion (4,6) to the left of dotted line 12, and an asynchronous portion (3) to the right thereof. The synchronous part of the circuit operates in synchronism with cell arrivals. It comprises a cell activity detector (not shown), which checks for active or idle cells, and two loops (4,6) which iteratively sum inter-arrival times and arrivals respectively and which introduce a "forgetfulness factor", i.e. a decay of the two sums. This decay is implemented by multiplying the respective sum by 2^-n, and has impact on the response of the estimator and its atcuracy. If n is large, the response of the estimator will be slow and, given time, accurate. If n is small, the response will be fast but noisy.

The asynchronous part may or may not operate in synchronism with cell arrivals. It carries out two divisions, yielding the estimate and the variance of the cell arrival rate.

It is assumed here for simplicity that a whole link is monitored, irrespective of VP and VC combinations, so incoming cells are checked for their idle or active status only. The estimator may however be applied to monitor separate VP and VC combinations.

In more detail, the estimator 2 includes a portion indicated at 4 which determines an arrival register value m_i+1, which is output at 10. A portion 6 is provided to which is input the measured inter-arrival times % and which determines a value for the inter- aπival time parameter S_i+1, which is output at 8. The portions 4, 6 are shown to the left hand side of dotted line 12, and are labelled as "synchronous" to indicate that the computations in portions 4, 6 should keep pace with the arrival of cells, as indicated by measured inter-arrival times t_i. On the other hand, the computational portion 3 illustrated to the right hand side of dotted line 12 is labelled as "asynchronous" to indicate that the computations performed thereby may proceed at a slower rate than those on the left hand side thereof, if necessary.

In order to more fully describe the operation of estimator 2, it will be assumed that several iterations of the estimating process have already been carried out, such that previous values of the arrival register value va^ and inter-arrival time parameter s_i are contained in feedback registers 24 and 22 respectively. With reference to equations (23) and (24), the portions 4, 6 are provided to determine current values for the arrival register value m_i+1 and inter-arrival time parameter S_i+1, respectively. Summing node 30 and multiplication node 26 constitute the means by which the response factor (1-2^-n) is implemented in the portion 6, and similarly summing node 32 and multiplication node 28 perform the equivalent function in portion 4. The previous value S_i of the inter-arrival time parameter is output from register 22 to nodes 26, 30 so as to be modified by the response factor, and the resulting output is fed to a summing node 16 where the present value of a measured inter-arrival time t_i is added thereto. The output of summing node 16 is temporarily stored at register 18, for subsequent output to the result calculation portion 3 and to feedback register 22. Portion 4 operates in a similar manner, with feedback register 24 outputting a previous value nij of the arrival register value to nodes 28, 32. The output of summing node 32 is directed to node 14 where the value is incremented, and the incremented value is temporarily stored in register 20 which holds the current arrival register value m_i+1. Output from register 20 is directed to result calculation portion 3 and to feedback register 24 for the next iteration. The result calculation portion 3 operates by receiving outputs 8, 10 from registers

18, 20 respectively. The inter-arrival time parameter value from register 18 then has added thereto an initial inter-arrival time value s_o at node 34. Similarly, the arrival register value from register 20 is incremented and summed with an initial arrival register value mo at node 36. To complete the estimation process a ratio is taken of the outputs from nodes 34 and 36 (which correspond the numerator and denominator of equation 43). The division is performed at node 38 and the estimation result E is stored in register 40. A variance may also be calculated by taking the ratio of the estimation E from register 40 and the output from node 34, which corresponds to the operation of equation 44. The response speed parameter n which is utilised in multiplication nodes 26, 28 of portions 6, 4 is a parameter which may be chosen by the operator of the estimator 2. The value of the response speed parameter n affects the stability and ability of the estimator 2 to respond to rapid changes in arrival rates. This is well illustrated by simulation results 110, 112, 114 and 116 shown in Figures 4a to 4d. In each of the graphs 110, 112, 114 and 116 a solid line represents the main traffic arrival rate from which the input data for the estimator 2 is formed, and a dotted lines graph the estimation output of arrival rate from the estimator 2. As indicated, graph 110 illustrates the estimation results of the estimator 2 in which the response speed parameter n = 4. Graph 112 is based on a response speed parameter of n = 6, graph 114 with n = 8, and graph 116 with n = 10. Throughout the stimulations, a Markov Modulated Poisson Process (MMPP) is used to generate stochastic traffic patterns. Such process consists of a set of states and within each state traffic is generated by a Poisson process whose mean rate is identified by the state value. The duration of and transitions between states are governed by Markov process, the traffic is fed into the estimator 2, which monitors the arrival of cells and their inter-arrival time, and updates its parameters m and s accordingly. Time is measured in the unit of time required to service a cell in an ATM switch. The arrival rate is normalised to the ATM link speed, which is 150 Mb/s. An estimation is made after every N cells have been received by the estimator. N can be chosen arbitrarily and it is set to 64 in this instance.

As noted in Equations (23) and (24), the estimation parameters s and m depend on the choice of the response speed parameter n. The effects of n on the estimation values are well illustrated by the graphs 110, 112, 114, 116 of Figure 4. When n is small (graph 110), the output of the estimator responds to change quickly but is very noisy. On the other hand, when n becomes larger (graph 116), the output of the estimator is less noisy but responds to the change very slowly. From these results, it is apparent that the dynamic behaviour of the estimator 2 is fully controlled by the parameter n, which may constitute a limitation of the estimator 2. That is, when n is small, the estimator can track changes in the input process but its output is not accurate. Conversely, when n is large, the estimator cannot track changes but its "steady state" output is very accurate. The estimator 50 illustrated in Figure 3 addresses this limitation by using two of such estimators 2, one with small n and the other with large n, and then selecting one of the outputs of the estimators 2 as the estimation output according to some heuristics. The resultant estimation output should have the desirable features of each individual estimation output, namely, responsive to changes and accurate. Referring to Figure 3, the estimator 50 is constructed as follows. Two estimators

2a and 2b are constructed essentially in accordance with the estimators 2 shown in Figure 2, and operate in parallel. Estimator 2a uses a response speed parameter n₁ which gives responsive output while estimator 2b uses a response speed parameter n₂ which gives low noise output. In the simulation studies discussed hεreinbelow n₁ is 6 and n₂ is 10. Where the elements of the individual estimators 2a and 2b of Figure 3 perform similar functions to the equivalent elements of the estimator 2 of Figure 2, similar reference numerals are used, and unless otherwise mentioned the estimators 2a and 2b operate in the same manner as estimator 2 described above. The estimator 50 additionally includes a delay register 96 which delays an estimator output value from output 100, and passes the delayed output value to a summing node 98, which produces a value indicative of the difference between the delayed output value from register 96 and an output value from estimator 2a. The difference value from node 98 is passed to a comparator 92 where it is compared with a threshold value T, input at line 94. The result of the comparison is then utilised by a multiplexer 90 and latch 84 in the following manner. Where the comparison indicates that the difference between delayed output 100 and the output of estimator 2a is greater than the threshold then the multiplexer 90 acts to pass the output from estimator 2a to the overall output 100. This is because such a comparison result indicates that a rapid change has taken place and therefore the responsive output of estimator 2a should be utilised as the output of estimator 50. Similarly, where the difference value is less than the threshold then the multiplexer 90 acts to take the output 100 from the output of estimator 2b, which gives a low noise output in the event of no rapid changes in traffic arrival rate. Additionally, whenever multiplexer 90 switches output 100 from the output of estimator 2b to the output of estimator 2a then latch 84 replaces the values held in feedback registers 22, 24 of register 2b with the values from feedback registers 22, 24 from register 2a. This is because whenever the output of estimator 50 is taken from estimator 2a, a change of state is implied, and the updated values from the responsive estimator 2a are therefore more accurate.

Graphs 120 and 122 illustrated in Figures 5a(i) and 5a(ii) shown a comparison between simulation results of the single parameter estimator 2 and the double parameter estimator 50 respectively. The choice of the threshold value T determines the maximum noise level that can be suppressed, and in this instance T is chosen to be 0.1. Graphs 124 and 126 show the same comparison as in 120 and 122, with different input traffic pattern data. As can be seen, the output of the double parameter estimator 50 (graphs 122, 126) tracks closely the input traffic process when compared with the single parameter simulation results (graphs 120, 124). Further, changes in arrival rate of the input traffic can be responded to quickly, and when the arrival rate stays at a level without change, the estimation output of the estimator 50 increases in accuracy. In considering the construction of circuitry to carry out the present invention, there are two basic implementation options. The first one considers the use of standard processing devices, such as Digital Signal Processors (DSP). The second involves custom VLSI implementation. The high speed computational capabilities of Digital Signal Processors (DSP) make them likely candidates for the implementation of the real time traffic estimator. Performance in this case will however be limited by the speed at which the various computations required by the estimator can be processed. The synchronous part of the real time traffic estimator, including the two loops

(4,6), the header checker and the inter-arrival time counter, can be considered as a sequence of fixed-point operations. Assuming that it requires approximately 25 instructions, and that the DSPs considered require one instruction cycle only for each instruction involved, the maximum bit rate that can be handled by the DSP can be computed.

The time t_s required for synchronous computations per cell is thus: 25 (instructions) x t_ic, where is t_ic the instruction cycle time of the DSP. The maximum bit rate will then be: 53 (octets) x 8 (bits) /t_s. For t_ic = 80 ns, the maximum bit rate is 210 Mbits/s. This is the maximum bit rate achievable for an AT&T manufactured floating point DSP32C processor chip and also a Texas Instruments manufactured fixed point TMS320C2x processor. In the latter case, even if a bit rate of 155 Mbits/s were considered, the remaining time until the next arrival would not allow the calculation of the estimate and the variance in the asynchronous part of the estimator. Clearly the maximum bit rate will be higher if the instruction cycle time decreases, or if less operations are needed. Nevertheless, this indicates a severe limitation if future bit rates of 622 Mbits/s and higher are to be considered.

The advantage of using a DSP resides in the use of a standard part to take care of the synchronous computations. The asynchronous computations may be done elsewhere, or in the case of the DSP32C, may be done in parallel in the floating point unit. If the maximum bit rate considered is limited to 50 Mbits/s, they could be carried out by the (low-end) DSP after the synchronous computations.

A custom implementation means that there is more than one solution to the implementation problem. The leverage in the architectural choice given by a custom VLSI implementation also leads to increased performance, and a fixed point or a floating point approach may be chosen for parts or all of the estimator. A custom VLSI implementation allows technology choice, such that GaAs could be selected to achieve very high bit rates in the GHz range. Clearly, the low maximum bit rate limitation seen in the case of a standard DSP implementation is overcome in a custom VLSI implementation.

The critical part of the implementation of the estimator is the real time processing required by the synchronous loops, and simulation results (not shown) have demonstrated that the simplicity of a fixed point processing approach is satisfactory.

As described hereinabove, the two loops in the synchronous part, for convenience dubbed "m loop" and "s loop" for the arrival count and the inter-arrival sum respectively, are similar in their implementation. Both have registers to hold the ith and i + 1th states, and a shifter to implement the multiplication by the "forgetfulness factor" (x2^-n). The result of the shift and the ith state are then fed to a subtracter. The result of the subtraction (1-2^-n), which is in fact the response factor, is held in an incrementable register in the case of the total sum of arrival (m loop). In the case of the inter-arrival sum, it is added to the inter-arrival time of the last active cell. The word length for the m loop may be chosen to be, for example, 13 bits. This is arrived at by considering the lowest acceptable exponent of the "forgetfulness factor", i.e. n = 4, which sets the number of digits after the implied fixed point, and the maximum value for m_i. This value is 2ⁿ, and a maximum acceptable value for n was taken as 8, as a larger value may cause the estimator to operate too slow for optimal performance. The word length for the s loop may be chosen as, for example, 16 bits.

The asynchronous part of the estimator requires two division operations: one each for the estimate and its variance. This can be implemented by using a divider circuit in sequence to yield the required outputs. Binary division is traditionally done by a repeated series of shift, subtract and compare cycles. The comparison operations make division by this method very slow. An algorithm involving a bit-level systolic carry-save array (H. Dawid and G. Fettweis, "Bit-level systolic carry-save array division", Proceedings, Globecom '92. pp. 484-488) may be an appropriate alternative for the implementation of the asynchronous divider. It is based on a non-restoring division, i.e. the remainder is not restored in the division cycle, and is not decision directed, i.e. avoids the comparison. It also lends itself to an efficient pipelining architecture. An alternative based on a self- timed divider (T. Williams, M. Horowitz, "A zero-overhead self-timed 160-ns 54-b CMOS divider", IEEE Journal of Solid-State Circuits, Vol. 26, No. 11, pp. 1651-1661, Nov. 1991) may also be considered.

The foregoing description has been put forward by way of example only, and many modifications will be apparent to those skilled in the art without departing from the spirit and scope of the invention, as defined in the claims appended hereto. APPENDIX A

We assume that we observe all arrivals to a queue and we are interested in estimating the arrival rate (service time is assumed to be known). The arrival rate will be modelled as a quantity with a randomly chosen value that is fixed over the time scale of interest.

However, the estimator will be constructed so that it may adapt to gradual changes in the value of arrival rate. The aim is to track a slowly time-varying arrival rate, with no distinction being made at this time between stochastic or deterministic variations in the

arrival rate. Let λ : arrival rate

T_1,...,m : sequence of observed inter-arrival times {t„ t₂, ..., t_m},

f(t_1,...,m|λ) : conditional probability density function (pdf) of a sequence of

observation (t_1, t₂, t₃, ..., t_m ) for a given value of λ, g(λ) : a priori pdf of λ.

h(λ |T_1,...,m ) : a posteriori pdf of λ.

Using the same assumption of Poisson arrivals, the pdf of a single observation is:

Pr(T_i ε [t_i, t_i + dt_i) |λ) = f(t_i| λ)dt = λe^-λtidt (1) and of a sequence of observations: f(T_1,...,m|λ) = ₌ λ^me ^-sλ (2)

where

The information about λ which can be extracted from the observations is represented by the conditional pdf of λ given t_2,...,m (Bayes Thorem), namely, ,

where k is the constant which normalises the pdf of λ, and g (λ) is the prior probability density function to be chosen.

Note that m and S are sufficient statistics of the observations for the parameter λ. All information on λ is derived from the observation s of m and S which may be recursively computer by the following equations: S_i+1 = S_i+T_i (5)

m_i+1 = m_i+1 (6)

So far λ has been treated as a constant. To allow for slow variation of λ, the recursive equations by which S_i and m_i are computed are modified as follows: S_i+1 = (1 - σ )S_i + MτΦ_iT _i (7)

m_i+1 = (1 - μ)m_i + MμΦ_i (8)

Φ_i is an indicator function which takes the value 1 if the ith observation is available, and 0 if it is not available (Φ_i can be set to 0 to "turn off" observations for a while), and σ, τ, μ, and M are free parameters which will be chosen to give the recursion suitable properties under a variety of conditions. We consider first the case where λ_i is equal to λ and Φ_i is one for all i. Since

S₀ = 0, (9)

s1 = T₁M τ, (10)

S₂ = (1 - σ)MτT₁ + MτT₂, (11) in general,

i-1

S_i = MτΣ

T_i-j(1 - σ)^j. (12) j=0 Similarly,

i-1

m_i = Mμ

(1 -μ)^j. (13)

Then, s - E{5_i} = Mτ∑βE{T_i}(1-σ)^j

= M [1 - (1 - σ)ⁱ] (14)

m = E{m_i = M[1 - (1 - μ)ⁱ] (15)

If we take the mode of the pdf with parameters s and m as a convenient estimator, then we want to ensure that (16)

So we require τ = σ = μ. The recursion can now be written as S_i+1 = (1 - μ)5_i + MμΦ_iT_i, (17)

m_i+1 = (1 - μ)m_i + MμΦ_i. (18)

For the parameter M, we will assume that the experimenter can choose a value which is related to the desired long-term accuracy of estimation, by the following reasoning. When lambda is fixed, the squared coefficient of variation df the pdf given by Equation (4) is equal to (m + 1)^-1, which is independent of s. Thus, if we choose a value of M, we are effectively choosing a target value for the squared coefficient of variation for the limiting conditional pdf of λ when the true value of λ is constant. We are nominatin g that the accuracy of our estimator (as measured by squared coefficient of variation) should approach the accuracy that would result from the observation of M independent, identically distributed negative exponential random variables.

Intuitively we would want S_i and m_i to approach zero, leaving us with only our prior information. As one possible choice, we may relate the rate of decay of S_i and m_i to the value of M. Recall that M was chosen so that if λ does not vary, the accuracy of the estimator will approach that of an estimator based on M independent identically distributed inter-arrival intervals. If we want the time constant for the decay of S, and m_i to also be equivalent to M inter-arrival intervals, we can choose μ so that

(1 - μ)^M = 1/e (19)

hence we want

M = -(1n(1 - μ))^-1 (20)

= (μ

+ 4 + ...)^-1 (21) For M large, this will be approximately satisfied if μ = 1/M. Because of the relative ease of multiplying or dividing by a power of 2, we will assume that M has been chosen as a power of 2 and denote log₂(M ) by n. The final form of the recursion is: S_i+1 = (1 - 2^-n)S_i + T_i (23) m_i+1 = (1 - 2^-n)m_i + 1 (24)

By choosing a natural conjugate prior pdf for λ we can simplify the computations required to choose the prior distribution parameters mo and S₀. Therefore we will assume that the prior pdf of λ can be adequately approximated by:- f(λ) = (25)

where m₀ and s₀ are chosen to represent any prior information. Note that the prior moments of λ are given in terms of the m₀ and s₀ by: 1

E{λ} =

Var{λ} =

also,

Mod{λ} =

e Hence it is a simple matter to choose m₀ and s₀ to match the first two moments of any given prior pdf which has finite positive mean and variance, as follows s₀ -

m₀ =

For example, suppose that our best prior information about λ comes from informed judgement of the maximum rate α that can be anticipated, and the average rate. For simplicity, we assume that λ takes the values α and 0 with probabilities θ and (1 - θ) respectively, where α and θ are known.

It is a simple matter to find a natural conjugate prior which matches the first two moments of this discrete prior, yet offers the advantage of retaining the natural conjugate form. Our discrete prior is:

P{λ = α} = θ

P{λ = 0} = 1 - θ (31)

hence

E{λ} = αθ (32)

Var{λ} = α²θ(1 - θ) (33)

The parameters of the natural conjugate prior which matches the first two moments of the discrete prior must therefore satisfy

Motivated by this example, we will rely on the simple equations 0

to approximate prior information which consists of estimated average and maximum arrival rates for a traffic stream.

At any stage i, we may compute the conditional pdf of λ from the values of s_i+1, m_i+1, s₀, and m₀. The mean and variance of this conditional pdf are easily computed from the above equations, namely f(λ|t_{1,..., m}) = V ^v

u 1

E(λ |t1_,...,m) ⁼

Var(λ|t_1,...,m)

Claims

1. Apparatus for estimating telecommumcations traffic in an asynchronous digital telecommumcations network comprising:

timing means to determine an inter-arrival time between cells;

an inter-arrival time register means for summing the inter-arrival time determined by the timing means with a previous inter-arrival time register value as modified by sai d response factor; and

2. Apparatus according to claim 1 wherein the arrival register means comprises an iterative loop which operates synchronously with respect to the arrival of cells at a node in said network.

3. Apparatus according to claim 1 or 2 wherein the inter-arrival time register means comprises an iterative loop which operates synchronously with respect to the arrival of cells at a node in said network.

4. Apparatus according to claim 2 wherein the arrival register iterative loop comprises a current arrival register, a previous arrival register which receives input from the current arrival register, a multiplication means for multiplying the previous arrival register value by a binary base raised to a negative integer power, a summing means for subtracting the multiplied result from the previous arrival register value, and an incrementing means for incrementing the subtracted result, the incremented value being stored in the current arrival register.

5. Apparatus according to claim 3 or 4 wherein the inter-arrival time register iterative loop comprises a current inter-arrival time register, a previous inter-arrival time register which receives input from the current inter-arrival time register, a multiplication means for multiplying the previous inter-arrival time register value by a binary base raised to a negative integer power, a first summing means for subtracting the multiplied result from the previous inter-arrival time register value, and a second summing means for summing the subtracted result with the inter-arrival time determined by the timing means, the summed result being stored in the current inter-arrival time register.

6. Apparatus according to claim 5 including a third summing means for adding an initial arrival register value estimate to the current arrival register value, a fourth summing means for adding an initial inter-arrival time value estimate to the current inter-arrival time value, and dividing means for producing a ratio of the results of the third and fourth summing means representative of the cell traffic estimate.

7. Apparatus according to claim 6 wherein the third and fourth summing means and the dividing means operate asynchronously with respect to the arrival of cells at said node.

8. An adaptive telecommumcations traffic estimator comprising first and second apparatus according to any one of claims 1 to 7, the first and second apparatus being provided with different response factors, and further comprising latch means to select the traffic estimate from one of the first and second apparatus in accordance with detected variations in the traffic estimates from the first and second apparatus.

9. A method for estimating telecommumcations traffic in an asynchronous digital telcommunications network comprising the recursive steps of:

10. A method as claimed in claim 9 wherein the response factor, K, has a valu e between 0 and 1, and wherein the inter-arrival time parameter S_i+1 is determined by adding the measured inter-arrival time t_i to the product of the response factor and the immediately preceding value of the inter-arrival time parameter, s_i, such that: s_i+1 = Ks_i + t_i

11. A method as claimed in claim 9 or 10 wherein the response factor K has a value between 0 and 1, and wherein the arrival register value m_i+1 is determined by incrementing the product of the response factor and the immediately preceding value of the arrival register value, m_i, such that m_i+1 =Km_i + 1

12. A method as claimed in claim 9, 10 or 11 wherein an initial arrival register value estimate is added to the arrival register value and an initial inter-arrival time value estimate is added to the inter-arrival time register value, prior to the ratio thereof being determined for the purposes of estimating cell traffic.

13. A method as claimed in claim 12 wherein the cell traffic estimate is determined according to

_{E =}

where E is the estimate of cell traffic and mo and s₀ are the estimated initial values for the arrival register value and inter-arrival time value respectively.

14. A method as claimed in any one of claims 9 to 13, wherein the value of the response speed parameter, which determines the value of the response factor, affects the speed at which the cell traffic estimate responds to changes in actual cell traffic in a real time recursive application of the method.

15. A method as claimed in claim 14 wherein the response factor K is calculated according to

K = (1 - 2^-n) where n is an integer value constituting said response speed parameter.

16. A method as claimed in claim 14 or 15 wherein first and second values of cell traffic are estimated using different respective values of the response speed parameter such that the first traffic estimate is characterised by a relatively faster response time as compared to the second traffic estimate, and wherein a final traffic estimate is based on the first traffic estimate when rapid changes in traffic are detected and otherwise based on the second traffic estimate.

17. A method as claimed in claim 16 wherein a said rapid change in traffic is detected by comparing a difference between the first traffic estimate and a previous value of the final traffic estimate with a threshold value.

18. A method as claimed in claim 16 or 17 wherein, following a said detected rapid change, a preceding value for the inter-arrival time value and arrival register value in respect of the second traffic estimate are substituted with corresponding values constituting the first traffic estimate.

19. A method as claimed in claim 9, 10 or 11 wherein the steps of determining the inter-arrival time value and determining the arrival register value are performed synchronously with respect to the arrival of cells at said node.

20. A method as claimed in claim 19 wherein the step of estimating cell traffic is performed asynchronously with respect to the arrival of cells at said node.

21. A method as claimed in claim 13, further including a step of estimating the variance, Var, of cell traffic at said node according to:

_Var .

V