CN115696451A - Optimization method for energy and task scheduling of edge computing system - Google Patents

Abstract

The invention relates to the field of Internet of things and discloses an optimization method for energy and task scheduling of an edge computing system, which comprises the following steps: the first step is as follows: based on a new energy and task scheduling protocol, the MEC system can be switched in an energy collection mode, an IRS auxiliary task unloading mode and an IRS standby task unloading mode in a self-adaptive manner according to the channel condition, the energy state of the IRS battery and the user task queue state; the second step is that: modeling a system optimization problem based on the developed protocol, and minimizing long-term task unloading and energy consumption calculation of a user; the third step: and decomposing the Lyapunov optimization method into a deterministic optimization problem based on time slots by using the Lyapunov optimization method, and solving the corresponding deterministic optimization problem by using a convex optimization theory.

Description

Optimization method for energy and task scheduling of edge computing system

Technical Field

The invention relates to the field of Internet of things, in particular to an optimization method for energy and task scheduling of an edge computing system.

Background

With the rapid spread of the internet of things, more and more IoT smart sensor nodes need to perform delay-sensitive, computationally intensive tasks. However, due to limited computational resources, it is often impractical or costly to accomplish these computational tasks locally on these nodes. As one of the emerging technologies of IoT, mobile edge computing can enable IoT nodes to offload their computing tasks to a server with sufficient computing resources for execution, and is expected to be an effective solution to the above-mentioned problems. And the MEC is deployed on the IoT, so that not only can the task execution delay be reduced, but also the energy consumption can be saved for IoT nodes. Therefore, how to design a good performance MEC system has attracted a great interest of scholars in recent years.

The intelligent reflector is an economic and efficient technology which is proposed in recent years and can realize a wireless communication system with high spectral efficiency. In a wireless communication system with an IRS, the phase shift of a passive element reflected signal is adjusted on the IRS, so that the received signal power of a wireless receiver can be improved. In an MEC system, by combining IRS technology, task offloading can be made more efficient, resulting in better system performance. Therefore, how to design an IRS-assisted MEC system has become a problem that has attracted intensive research interest of researchers in recent years.

The document 1[ T.Bai, C.Pan, Y.Deng, M.Elkashlan, A.Nallanathan and L.Handzo, "tension Minimization for Intelligent reflection Surface air end Mobile Edge Computing," IEEE Journal on Selected Areas in Communications, vol.38, no.11, pp.2666-2682, nov.2020] investigated the benefits of deploying IRS in MEC systems, where multiple devices offload tasks to Edge compute nodes through IRS, with the goal of minimizing Latency under Edge compute capability constraints and IRS phase shift constraints.

In most of the prior studies it was assumed that the IRS was powered by a battery or the grid, so that the phase shift of the passive elements could be adjusted by the controller. However, replacing or recharging batteries is often costly and inconvenient, and may not even be practical in harsh environments or special application scenarios, and thus the operational lifetime of an IRS powered by batteries is easily limited by the battery capacity. If a fixed power supply is used for supplying power, the IRS can only be deployed at a position where a fixed power grid can be accessed, and the IRS cannot be used in many occasions without power grid access. Wireless radio frequency energy harvesting is a new technology that enables a wireless node equipped with a radio frequency energy harvesting circuit to harvest energy from RF signals to extend its operating life, and therefore wireless powered IRS assisted wireless communication systems incorporating radio frequency energy harvesting technology have recently received a lot of attention from scholars.

Document 2, s.xu, y.du, j.liu and j.li, "Intelligent reflection surface based feedback communication for data streaming," IEEE trans.communication ", to be public, doi:10.1109/tcomm.2022.3170629 ] studies assume that an IRS is connected to a user terminal and helps the user terminal to offload task data to a plurality of MEC servers for cooperative calculation, and energy consumed by the IRS operation and user local calculation is obtained from an RF signal emitted from a power beacon.

Documents 3, s.moo, n.zhang, l.liu, j.wu, m.dong, k.ota, t.lui, and d.wu, "computing rate knowledge for interactive reflected surface enhanced wireless power transmitted mobile computing networks," IEEE trans.v. eh.technol., vol.70, no.10, pp.10820-10831, oct.2021 ] assume that the IRS and all user terminals are powered by energy collected from the RF signal transmitted from the base station, and the IRS uses the collected energy to assist the user terminals in offloading task data to the base station.

The problems of the prior art are as follows: in the prior researches, such as documents [2-3], for the simplicity of analysis, it is assumed that the calculation task generated at the user terminal at the beginning of a time slot must be completed at the current time slot, and the energy scheduling adopts the collection-use strategy adopted by most wireless energy supply systems, that is, the energy collected by the IRS at a time slot must be completely used up at the current time slot. However, the HTU method does not increase the amount of energy harvested in a limited time frame and does not make efficient use of the harvested energy at the IRS end.

Based on the above analysis, a design scheme different from the documents [2-3] needs to be studied to increase the energy collected by the IRS and efficiently utilize the collected energy, thereby improving the system performance. Therefore, firstly, a new energy and task scheduling protocol is proposed, so that the MEC system can adaptively switch among three modes (i.e. an energy collection mode, an IRS auxiliary task offloading mode and an IRS standby task offloading mode) according to the channel condition, the energy state of the IRS battery and the user task queue state. In the energy harvesting mode, the IRS may accumulate harvested energy to be used in subsequent time slots; in the IRS auxiliary task unloading mode, the user side unloads task data to the HAP under the assistance of the IRS; in the IRS standby task offload mode, the IRS is in a standby state (i.e., no more energy is used), and the ue only offloads task data to the HAP through the direct link.

Due to the randomness of the arrival of wireless channels and tasks and the correlation between the system working mode and the resource allocation decision of each time slot, the established problem is a random optimization problem of multi-stage sequence decision and is difficult to directly solve, and therefore, the optimization method for the energy and task scheduling of the edge computing system is provided.

Disclosure of Invention

Technical problem to be solved

Aiming at the defects of the prior art, the invention provides an optimization method for energy and task scheduling of an edge computing system, which solves the problems.

(II) technical scheme

In order to achieve the above purpose, the invention provides the following technical scheme: an optimization method for energy and task scheduling of an edge computing system comprises the following steps:

the first step is as follows: based on a new energy and task scheduling protocol, the MEC system can be switched in an energy collection mode, an IRS auxiliary task unloading mode and an IRS standby task unloading mode in a self-adaptive manner according to the channel condition, the energy state of the IRS battery and the user task queue state;

the second step is that: modeling a system optimization problem based on the developed protocol, and minimizing long-term task unloading and energy consumption calculation of a user;

the third step: and decomposing the Lyapunov optimization method into a deterministic optimization problem based on time slots by using the Lyapunov optimization method, and solving the corresponding deterministic optimization problem by using a convex optimization theory.

Preferably, the specific steps in the first step are as follows:

s1: establishing a channel model;

taking a channel in an MEC system as a quasi-static channel;

the user side can unload the calculation task data to the HAP through the UA link and the URA link;

UA link, the channel coefficient in slot k being denoted h _UA (k) And modeling it as Rayleigh fading, i.e.

Where ρ is ₀ Is a reference distance d ₀ Path loss at =1m, α _UA Is the corresponding path loss exponent, d, of the UA channel link _UA Is the distance between the user terminal and the HAP,

is a complex gaussian random scattering component of zero mean and unit variance;

URA links including two channel links of user end to IRS (UR, user-to-IRS) and IRS to HAP (RA, IRS-to-HAP), wherein channel coefficient vectors in time slot k are uniformly expressed as

Wherein ab ∈ { UR, RA }, alpha _ab Is the channel path loss exponent from node a to node b, d _ab Is the distance between node a and node b, ζ _ab Is the rice factor associated with small scale fading,

is the response vector of the ULA array and,

is a complex matrix of I rows and J columns in

Middle diameter phi _ab (k) Expressed as angle of arrival or angle of departure of the respective signal, (. Cndot.) ^T Indicated as a result of the transpose operation,

is a non-direct component in a rice fading channel, each element of which is a random scattering component of zero mean and unit variance;

is provided with

Represents the reflection vector of IRS in slot k, where θ _n (k) Is the phase shift of the nth reflection unit, the reflection amplitude coefficient for each reflection unit is set to the maximum value that can be reached, so as to maximize the signal reflection power, and therefore, the reflection coefficient of the IRS should satisfy the following constraint:

s2: the wireless power supply IRS assists the task unloading protocol;

the MEC system under the new protocol can be operated in an energy collection mode, an IRS auxiliary task unloading mode and an IRS standby task unloading mode, wherein t _e (k) And t _o (k) In the three modes, users can locally execute part of calculation tasks within the duration of the whole time slot, and the calculation task unloading of the users and the energy collection of the IRS can not be carried out simultaneously;

in a time slot _k The following equation holds true: phi is a _I (k)t _e (k)+φ _II (k)(t _e (k)+t _o (k))+φ _III (k)t _o (k)＝T。

Preferably, in the energy collection mode, all the time in one time slot is used for the energy collection of the IRS, in this case, the HAP transmits RF energy signals to the IRS, and the IRS collects energy from the RF energy signals, and in this mode, the user side does not offload computation task data to the HAP, and only relies on itself to perform the computation task locally;

in an IRS auxiliary task unloading mode, dividing a time slot into two stages, and in the first stage, the IRS collects energy; in the second stage, the ue offloads the task data to the HAP with the assistance of the IRS, as a specific example, in this mode, when the initial energy of the IRS is sufficient, the first stage may not exist, and the IRS offloads the task data to the HAP at the time of the whole timeslot, that is, t is _e =0 and t _o ＝T；

In the IRS standby task offload mode, the user only offloads the computing task data to the HAP through the UA link, and the IRS is in a standby state with power off, which is selected in the following two cases: firstly, when the battery energy of the IRS is insufficient, the IRS can not participate in auxiliary task unloading, and secondly, when the channel quality of the UA link of the current time slot is good, a user can directly unload a calculation task to the HAP through the UA link.

Preferably, the second step comprises the following specific steps:

s1: the energy consumption model of the user comprises energy consumption of task unloading and energy consumption of task local calculation;

s2: an IRS energy collection and consumption model;

the IRS collects energy from the RF energy signal transmitted by the HAP in an energy collection mode and an IRS-assisted task offloading mode, and the energy collected by the IRS in slot k can be expressed as

In IRS-assisted task offloading mode, the energy consumed by the available IRS in slot k is E _C (k)＝μNφ _II (k)t _o (k)；

Preferably, the energy consumption for task offloading includes:

when the system operates in the IRS auxiliary task unloading mode, the maximum achievable data transmission rate is as follows:

b is the bandwidth of the system, p (k) is the transmit power of the user terminal, σ ² Is the additive white gaussian noise power at the HAP. Let d (k) be t _o (k) The amount of task data offloaded during the period;

the energy consumption of the user side for executing task unloading is as follows:

when the IRS operates in the standby task unloading mode, the energy consumed by the user side for unloading the d (k) task data volume is energy;

s3: and problem modeling is carried out, and when a user side processes a computing task, the computing task amount in the task queue can be scheduled in a time period. The user task queue state is represented as Q (k) at the beginning of slot k, at the end of slot k or at an equivalent time instant (k + 1) ^- Expressing the user task queue state as Q (k + 1), the user executes local calculation under three modes, executes task unloading under an IRS auxiliary task unloading mode and an IRS standby task unloading mode, and D (k) is the data volume of the task executed and unloaded locally by the user end in the time slot k, so that the user end has the task data volume

Preferably, the third step comprises the following specific steps:

s1: defining a virtual energy state based on the energy state B (k) of the IRS battery:

X(k)＝B(k)-G；

s2: where G =2TN μ is a time-independent constant described as:

X(k+1)＝X(k)+E _H (k)-E _C (k)；

s3: defining a quadratic lyapunov function as:

s4: introducing a Lyapunov drift function delta (omega (k)):

s5: further defining a Lyapunov drift penalty function obtained by weighting the Lyapunov drift function and the objective function of the deterministic optimization problem:

wherein λ is a non-negative weighting factor;

s6: theorem upper bound of lyapunov drift penalty function:

m is a finite constant independent of λ;

s7: the optimization target is rewritten into a Lyapunov drift penalty function from a target function of the problem, and the original problem can be converted into a problem of solving the minimum value of the upper bound by utilizing the upper bound of the drift penalty function:

φ _I (k)t _e (k)+φ _II (k)(t _e (k)+t _o (k))+φ _III (k)t _o (k)＝T

d(k)≥0,l(k)≥0,T≥τ(k)≥0；

s8: determining an optimal system working mode based on a problem solving and system optimizing algorithm so as to obtain an optimal solution of the problem with the minimum value;

when phi is _I (k) When =1, the system operates in energy collection mode, and the problem of the minimum value can be abbreviated as:

s.t.l(k)≥0；

the objective function is O (k), square equation

Solving, and combining a constraint condition l (k) to be more than or equal to 0 to obtain the optimal solution of the optimization variable l (k);

when phi is _II (k) When =1, the system is operating in the IRS-assisted task offload mode, let Ψ' (k) = { d (k), l (k), t (k), Θ (k) }, the problem of the minimum value can be rewritten as

d(k)≥0,l(k)≥0,T≥τ(k)≥0；

S9: due to the fact that

The optimal solution for the optimization variable Θ (k) can thus be found as:

wherein

In obtaining l ^* (k) And theta ^* (k) Then, the following problem can be simplified:

s.t.d(k)≥0,T≥τ(k)≥0；

s10, solving the problems to obtain an optimal solution, and determining Y _m (k) (m ∈ { I, II, III }) so that the optimal system operating mode for the kth slot can be determined as follows:

preferably, the system optimization algorithm comprises the following steps:

s1: initialization: k =1;

S2：while TRUE；

s3: acquiring system channel state information CSI of a kth time slot, and reading energy state information B (k) of an IRS battery and user task queue state information Q (k);

s4: solving for threeObtaining the optimal solution of d (k), l (k), t (k) and theta (k) by the optimization problem corresponding to each mode, and calculating Y _m (k)；

S5: determining system working mode m ^* (k)；

S6: according to m ^* (k) And the optimal solution of d (k), l (k), t (k) and theta (k) in the corresponding system working mode, performing optimal resource allocation, and updating queue states B (k + 1) and Q (k + 1) of the next time slot;

S7：k＝k+1；

S8：end while。

(III) advantageous effects

Compared with the prior art, the invention provides an optimization method for energy and task scheduling of an edge computing system, which has the following beneficial effects:

1. compared with the four reference schemes, the optimization method for the energy and task scheduling of the edge computing system has the lowest energy consumption, specifically, compared with the short-sight scheme, the energy consumption of the system of the scheme is only 10% -50% of the energy consumption of the system, and compared with the local computing scheme and the HAP-only computing scheme, the energy consumption is saved more, so that the energy consumption of a user end can be obviously saved by using the new protocol and the system optimization algorithm provided by the scheme.

2. According to the optimization method for energy and task scheduling of the edge computing system, when the path loss index is increased from 2.5 to 5, the energy consumption of the scheme without the IRS assistance is increased by about 22 times, while the energy consumption of the scheme provided by the invention is only increased by about 2 times, so that the energy consumption of a user end can be obviously saved by deploying the IRS in the system. Meanwhile, for the HAP-only calculation scheme, when the path loss exponent is increased from 2.5 to 5, the consumed energy is increased by about 6 times, thereby verifying that the energy consumption of the user terminal can be saved by using a partial offloading mode. Furthermore, the energy consumption performance of the proposed scheme is also significantly better than that of the short-view scheme for all UA link path loss indexes, thus further verifying that better energy consumption performance can be obtained using the new protocol and optimization algorithm proposed herein than the energy and task scheduling approach of documents [2-3 ].

Drawings

FIG. 1 is a schematic diagram of a wirelessly powered IRS assisted MEC system;

FIG. 2 is a schematic diagram of three system operation modes in the proposed task offload protocol;

FIG. 3 is a diagram illustrating the comparison of energy consumption performance of various schemes when the transmission power of the HAP is changed;

fig. 4 is a schematic diagram illustrating comparison of energy consumption performance of different schemes when the channel quality of the UA link changes;

fig. 5 is a schematic flow chart of the system optimization algorithm.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Consider that in the wirelessly powered IRS assisted MEC system shown in fig. 1, the computing tasks to be executed arrive randomly at the user end, and since the user end has limited computing power, part of the computing tasks needs to be offloaded to the HAP for cooperative computing. Meanwhile, assuming that there is an obstacle between the ue and the HAP, the quality of the channel link from the ue to the HAP (UA) is poor, and an IRS needs to be deployed between the ue and the HAP to improve the performance of the ue in offloading the computing task. In other words, the HAP may receive task data from the user side through the UA link and the URA (user → IRS → HAP) link at the same time. It is assumed herein that the IRS consists of a Uniform Linear Array (ULA) with N reflective elements, a controller that can adjust the phase shift of each reflective element, a radio frequency energy harvesting circuit, and a rechargeable battery. Wherein the IRS collects the rf signal energy emitted from the HAP through the rf energy harvesting circuit, stores it in the rechargeable battery, and then uses this stored energy for signal reflection operations. In addition, since the transmit power of the user end is usually much lower than that of the HAP, the energy obtained by the IRS from the signal transmitted by the user end is ignored herein.

In the MEC system under consideration, it is assumed that the user's task arrival and execution model is described as follows. Assume that the system is operating on a slot basis and considers a time period of length K x T, where K is the number of slots and T is the length of each slot. In each time slot

At the beginning, new computing tasks arrive at the user end, and the computing tasks are buffered in a computing task buffer queue at the user end. The client processes these computing tasks according to the FIFO. The size of the data volume of the calculation task reaching the user end in each time slot is represented as A (k) being more than or equal to 0, and the average value of the data volume of the calculation task is assumed to be A _mean ＝A _max A uniform distribution of/2, i.e.

Wherein A is _max The maximum amount of computational tasks that arrive for each time slot. For convenience of analysis, it is assumed herein that the user side calculates the length of the task buffer queue to be infinite; however, in subsequent simulations, the queue length required for verification will not exceed an upper bound, and therefore the algorithm designed herein can also be applied to situations where user queue buffer capacity is limited.

An optimization method for energy and task scheduling of an edge computing system comprises the following steps:

s1, in the wireless-powered IRS-assisted MEC system studied herein, to increase the energy collected by the IRS and efficiently utilize the collected energy, thereby improving the system performance, a new energy and task scheduling protocol is proposed, so that the MEC system can adaptively switch among three modes (i.e., an energy collection mode, an IRS-assisted task offload mode, and an IRS-standby task offload mode) according to the channel condition, the energy state of the IRS battery, and the user task queue state.

Specifically, the step S1 includes the following steps:

s11, channel model

The channel in the MEC system is assumed herein to be a quasi-static channel, i.e. constant within a single time slot, but may vary independently in different time slots. Furthermore, each task offload from the user side to the HAP is done in a single time slot. That is, at the beginning of each timeslot, the ue will decide whether and how to offload its computing task data to the HAP.

As described in the previous subsection, the client may offload computing task data to the HAP over UA and URA links. For the UA link, the channel coefficient in slot k is denoted as h _UA (k) And modeling it as Rayleigh fading, i.e.

Where ρ is ₀ Is a reference distance d ₀ Path loss at =1m, α _UA Is the corresponding path loss exponent, d, of the UA channel link _UA Is the distance between the user terminal and the HAP,

is a complex gaussian random scatter component of zero mean and unit variance. For URA link, including two channel links of user end to IRS (UR, user-to-IRS) and IRS to HAP (RA, IRS-to-HAP), channel coefficient vectors in time slot k are collectively expressed as

Wherein ab ∈ { UR, RA }, alpha _ab Is the channel path loss exponent from node a to node b, d _ab Is the distance between node a and node b, ζ _ab Is the rice factor associated with small scale fading,

is the ULA array response vector and,

a complex matrix of I rows and J columns; in that

Middle phi _ab (k) Expressed as angle of arrival or angle of departure of the respective signal, (-) ^T As indicated by the operation of the transpose,

is the non-direct component in the rice fading channel, each element of which is a random scattered component of zero mean and unit variance.

In addition, let

Represents the reflection vector of IRS in slot k, where θ _n (k) Is the phase shift of the nth reflecting element. The reflection amplitude coefficient for each reflection unit is set to a maximum value that can be reached to maximize the signal reflected power. Thus, the reflection coefficient of the IRS should satisfy the following constraint:

in practical applications, the phase shift of the IRS is typically a discrete value. However, to simplify the analysis, the assumption of most current IRS-related studies is used herein, i.e. the assumption that the reflected phase shift of the IRS is continuous.

Since the URA link is obtained by connecting the UR link, the IRS reflection phase shift and the RA link in series, the channel coefficient of the URA link can be expressed as k

Where Θ (k) is a diagonal matrix, i.e., Θ (k) = diag (θ (k)). Thus, at time slot k, when a user offloads computational task data to the HAP via UA and URA links, its offloading equivalent combined channel coefficients can be expressed as

As previously mentioned, IRS uses the energy collected from the RF signal transmitted by the HAP. Given the hardware implementation feasibility and cost considerations, it is assumed herein that the IRS uses a single antenna independent of the reflective element for energy harvesting. In slot k, the link channel coefficient of the HAP to IRS (AR, HAP-to-IRS) is denoted as g _AR (k) Which obey a Rice distribution, i.e.

Wherein alpha is _AR Is the corresponding path loss exponent, d, of the AR link _AR Indicating the distance between the HAP and the IRS,

representing the random scatter component.

S12, wireless power supply IRS auxiliary task unloading protocol

To efficiently utilize the time-varying nature of the wireless channel for energy harvesting and to efficiently use the harvested energy, a new task offloading protocol is proposed herein for a wireless-powered IRS assisted MEC system. In documents [2-3]]In this case, the IRS must use up all available energy at the end of each slot, and the computation tasks generated at the user end must be completed within one slot. In contrast, the new protocol proposed herein enables the IRS to adaptively perform energy and task scheduling based on the channel quality of the system link, the energy state of the IRS battery, and the user task queue state. Specifically, the MEC system under the new protocol may operate in three modes (i.e., energy collection mode, IRS auxiliary task offload mode, and IRS standby task offload mode) as shown in fig. 2, where t _e (k) And t _o (k) The time length used for the IRS to collect energy and the time length from the user side to the HAP are respectively used in one time slot k, and T is the length of one time slot. For convenience of description, the three modes in fig. 2 (a) - (c) are respectively referred to as mode I, mode II and mode III. In the three modes shown in fig. 2, the user will perform part of the computation task locally for the duration of the whole time slot, and the user's computation task offloading and the IRS's energy harvesting cannot be done simultaneously.

In mode I, all the time in one slot is used for the energy harvesting of the IRS. In this case, the HAP transmits RF energy signals to the IRS, from which the IRS collects energy. Meanwhile, in this mode, the ue does not offload the computing task data to the HAP, but only relies on itself to execute the computing task locally.

In mode II, a slot is divided into twoAnd (5) stage. In the first stage, the IRS performs energy harvesting; in the second stage, the client offloads the computing task data to the HAP with the assistance of the IRS. As one specific example, in this mode, the first phase may not be present when the initial energy of the IRS is sufficient; at this time, the IRS unloads the computing task data to the HAP at the auxiliary user end in the whole time slot, namely t is _e =0 and t _o ＝T。

In mode III, the user offloads the computing task data to the HAP only through the UA link, and the IRS is in a standby state with power off. This mode is selected in two cases: firstly, when the battery energy of the IRS is insufficient, the IRS cannot participate in auxiliary task unloading; secondly, when the channel quality of the UA link of the current time slot is good, the user can directly unload the calculation task to the HAP through the UA link, so that the energy of the IRS is saved, and the user can use the IRS in the subsequent time slot.

The set of the three MEC system working modes is recorded as

Let phi _m (k) E {0,1} as an operation mode indicator, wherein

When phi is _m (k) =1, the MEC system operates in mode m in time slot k. In a time slot, the system can only select one operation mode, so that there is

According to FIG. 2, when the MEC system is operating in mode I, t _e (k)＝T，t _o (k) =0; when the MEC system is operating in mode II, t _e (k)＝T-τ(k)，t _o (k) = τ (k); when the MEC system is operating in mode III, t _e (k)＝0，t _o (k) And = T. Thus, at slot k, the following equation holds:

φ _I (k)t _e (k)+φ _II (k)(t _e (k)+t _o (k))+φ _III (k)t _o (k)＝T (2)

generally, a user side executes a computing task through an MEC server through three stages of task unloading, remote execution and result downloading. Since the time for task remote execution and result downloading is usually much shorter than the time for task unloading, the two stages of task remote execution and result downloading are omitted here, and the first stage of task unloading is focused on. For many computationally intensive internet of things applications (e.g., image/video/voice recognition, file scanning, data analysis, multi-sensor information processing, etc.), this assumption is reasonable since MEC servers deployed at HAPs typically have more abundant computing resources than clients, while the amount of computing result data is typically much less than the amount of task input data.

S2, modeling is carried out on the system optimization problem based on the developed protocol, and the long-term task unloading and the calculation energy consumption of a user are minimized;

specifically, the step S2 includes the following steps:

s21, energy consumption model of user

1) Energy consumption of task offloading: according to the relevant protocols described in the previous section, when the MEC system is operating in mode II, the user side can offload task data to the HAP over UA and URA links. Wherein the maximum achievable data transmission rate is

Where B is the bandwidth of the system, p (k) is the transmit power of the user terminal, σ ² Is the additive white gaussian noise power at the HAP. Let d (k) be t _o (k) During which the amount of task data to offload. Therefore, the energy consumption of the ue performing task offloading in this mode can be obtained as

When the MEC system is operating in mode III, the user only offloads task data to the HAP through the UA link. Therefore, similar to the derivation of (4), the energy consumed by the UE to unload the data amount of the d (k) task in the available mode III is

2) Energy consumption of task local computation: let C ≧ 0 be the number of Central Processing Unit (CPU) cycles required for the client to execute one bit of the computational task, which generally depends on the type of computational task and the CPU architecture of the client. Further, the task input bit for the client to perform local computation in slot k is denoted as l (k). It can be shown that to save power consumption, the client should perform local calculations in slot k with a constant CPU frequency Cl (k)/T using dynamic voltage and frequency scaling techniques. Therefore, in time slot k, the energy consumption of the client to perform local computation can be expressed as

Where ζ > 0 represents the effective switched capacitance coefficient, which depends on the CPU chip architecture at the user side.

Based on the above analysis, the total energy consumption of the ue in the time slot k can be expressed as

S22, IRS energy collection and consumption model

As shown in fig. 2, the IRS collects energy from the RF energy signal transmitted by the HAP in mode I and mode II. Let η E (0,1) denote the energy collection efficiency, P _A Representing the transmit power of the HAP. Thus, the energy collected by the IRS in slot k may be expressed as

Furthermore, in mode II, the IRS is energy consuming in assisting the user in reflecting the computing task data signal to the HAP.In general, the power consumption of an IRS increases linearly with the size of the IRS and depends on the phase resolution of the individual reflective elements. Let μ denote the power consumption of a single reflective element, which is related to the phase resolution. Thus, the energy consumed by IRS in time slot k is obtained as E _C (k)＝μNφ _II (k)t _o (k)。

S23, problem modeling

As described above, when the user side processes the computing task, the amount of the computing task in the task queue may be scheduled within a time period. At the beginning of time slot k (denoted as time instant k) ^- ) Representing the user task queue state (i.e. the number of bits stored in the user side computation task data buffer) as Q (k); at the end of time slot k or equivalent time instant (k + 1) ^- The user task queue state is denoted as Q (k + 1). According to the protocol shown in FIG. 2, the user performs local computations in all three modes, and task offloading in mode II and mode III. Let D (k) be the amount of task data that the user end executes and offloads locally in time slot k, then there is

Note that the size of a new computation task that arrives at the user side at the beginning of slot k is a (k). Thus, the user task queue state change should satisfy the following equation:

Q(k+1)＝max{Q(k)+A(k)-D(k),0} (8)

meanwhile, stability is an important indicator for characterizing the user's task queue buffer, which means that the average task execution should not exceed the time-average task arrival rate, i.e. the stability is an important indicator

Similar to Q (k), the energy state of the IRS battery at the beginning of time slot k is represented as B (k) ≧ 0. According to the task offload protocol described above, at the end of time slot k, a portion of energy may remain in the battery of the IRS for use in the next time slot (k + 1). Thus, the end of time slot k (i.e., time instant (k + 1)) ^- ) Of IRS cellsThe energy state is represented by B (k + 1) ≧ 0. Therefore, the energy state evolution of the IRS battery should satisfy the following equation:

B(k+1)＝B(k)+E _H (k)-E _C (k) (10)

at the same time, the IRS should not consume more than its collected average energy over an extended period of time, i.e.

For the wirelessly powered IRS assisted MEC system shown in fig. 1, the goal herein is to optimize the system operating mode per timeslot, the task scheduling for the user, the IRS reflection phase shift and time allocation in mode II (i.e., Ψ (k) = { Φ (k), d (k), l (k), t (k), Θ (k) }, where Φ (k) = { Φ (k) = [ #) Φ (k), l (k), t (k), Θ (k) } _I (k),φ _II (k),φ _III (k)}，t(k)＝{t _e (k),t _o (k) }) to minimize the average energy consumption of the user side for task computation and offloading, i.e. to minimize the average energy consumption of the user side for task computation and offloading

The energy consumption minimization problem studied herein can be expressed as the IRS reflection coefficient constraint in (1), the time allocation constraint in (2), the long-term average task scheduling constraint in (9), and the long-term average energy scheduling constraint in (11)

C ₂ :φ _I (k)t _e (k)+φ _II (k)(t _e (k)+t _o (k))

+φ _III (k)t _o (k)＝T

C ₆ :d(k)≥0,l(k)≥0,T≥τ(k)≥0 (12)

In the problem (12), since the radio channel and the amount of arriving tasks in each slot are random, the channel state information and the task state information of the subsequent slots (i.e., slots k +1, k +2, … …) cannot be determined in slot k. Therefore, the problem (12) is a classical random optimization problem, which is difficult to solve directly. In order to solve the problem, the method is decomposed into a series of mutually independent deterministic optimization problems among time slots based on a Lyapunov optimization method, and the corresponding deterministic optimization problems are solved through a convex optimization theory, so that a low-complexity efficient algorithm is provided.

And S3, decomposing the Lyapunov (Lyapunov) optimization method into a deterministic optimization problem based on time slots by using the Lyapunov optimization method, and solving the corresponding deterministic optimization problem by using a convex optimization theory, thereby providing a low-complexity efficient online algorithm.

Specifically, the step S3 includes the following steps:

s31, problem transformation

To solve the problem (12) using the lyapunov optimization method, a virtual energy state is first defined based on the energy state B (k) of the IRS battery:

X(k)＝B(k)-G (13)

where G =2TN μ is a time-independent constant. As can be seen from formula (13), although B (k) ≧ 0, X (k) may take a negative value. According to equation (10), the change in state of X (k) can be described as

X(k+1)＝X(k)+E _H (k)-E _C (k) (14)

In the literature, it has been demonstrated that ensuring the stability of queue X (k) is equivalent to satisfying the long-term average energy scheduling constraint C4 in problem (12).

Let Ω (k) = [ Q (k), X (k) ] be a generalized queue based on Q (k) and X (k). Thus, a quadratic Lyapunov function can be defined as

Where v is a non-negative constant that acts to make the values of Q (k) and X (k) the same order of magnitude. Further, in order to ensure the stability of the generalized queue Ω (k), a lyapunov drift function Δ (Ω (k)) is introduced:

which reflects the amount of change from slot k to slot (k + 1) generalized queue omega (k).

Based on the Lyapunov optimization theory, a Lyapunov drift penalty function obtained by weighting the Lyapunov drift function and the objective function of the problem (12), i.e., a Lyapunov drift penalty function, can be further defined

Where λ is a non-negative weighting factor.

To further simplify the optimization problem, the following theorem gives an upper bound on the Lyapunov drift penalty function.

The upper bound of the lyapunov drift penalty function for each slot can be determined by the following expression.

Where M is a finite constant independent of λ, and can be written as

According to the Lyapunov optimization method, the optimization target can be rewritten from the target function of the problem (12) to a Lyapunov drift penalty function, so that the system energy consumption is minimized while the stability of a system queue is ensured. Further, using the upper bound of the drift penalty function in equation (18), the original problem can be transformed into a problem that solves the minimum of the upper bound, i.e., the problem is solved

φ _I (k)t _e (k)+φ _II (k)(t _e (k)+t _o (k))+φ _III (k)t _o (k)＝T

d(k)≥0,l(k)≥0,T≥τ(k)≥0 (20)

The problem (20) involves solving the optimization variables for only one slot (i.e., the k-th slot) as opposed to the problem (12) requiring solving the optimization variables for multiple slots, and is therefore a relatively easy to handle problem.

S32, problem solving and system optimizing algorithm

For solving the problem (20), it is noted that the optimization variable system operation mode indicator phi (k) is a binary optimization variable, but since there are only three system operation modes, the optimal solution of the problem (20) can be obtained by respectively solving the corresponding optimization problems in the three system operation modes and then determining the optimal system operation mode.

When phi is _I (k) =1, the system is operated in energy collection mode, and the problem (20) can be abbreviated as

s.t.l(k)≥0 (21)

Note that the problem (21) objective function is O (k). Equation of pairs

Solving is carried out, and the optimal solution of the optimized variable l (k) can be obtained by combining the constraint condition l (k) being more than or equal to 0

When phi is _II (k) And when =1, the system works in an IRS auxiliary task unloading mode. Let Ψ' (k) = { d (k), l (k), t (k), Θ (k) }, the problem (20) may be rewritten as

d(k)≥0,l(k)≥0,T≥τ(k)≥0 (23)

Similar to the method for solving the l (k) optimal solution in equation (22), the l (k) optimal solution in problem (23) can be obtained. Further, it is noted that the optimal solution for the optimization variables Θ (k) can be maximized by maximizing

Thus obtaining the product. Due to the fact that

The optimal solution for the optimization variable Θ (k) can thus be derived as

Wherein

In obtaining l ^* (k) And theta ^* (k) Then, the problem (23) can be simplified to the following problem:

s.t.d(k)≥0,T≥τ(k)≥0 (25)

to solve the problem (25), it is discussed in two cases:

(1) when X (k) is equal to or greater than 0, the optimal solution of the optimization variable tau (k) can be derived

τ ^* (k)＝T (26)

Based on equation (26), the optimal solution of the obtainable optimization variable d (k) is

(2) When X (k)<At 0, a relaxation variable is introduced

Thus, the problem (25) can be rewritten as

s.t.d(k)≥0,T≥τ(k)≥0

d(k)log(2)≤-τ(k)Blog ₂ (τ(k)B/z) (28)

It can be shown that the problem (28) is a convex problem. Thus, an optimal solution to the problem can be obtained by the interior point method.

When phi is _III (k) And when =1, the system works in an IRS standby task unloading mode. Thus, the problem (20) can be rewritten as

s.t.d(k)≥0,l(k)≥0 (29)

Similar to the method for solving the optimal solutions for l (k) and d (k) in equations (22) and (25), the optimal solutions for l (k) and d (k) in problem (29) can be obtained.

After the optimal solution of problems (21), (23) and (29) is found, Y can be determined _m (k) (m ∈ { I, II, III }) so that the optimal system operating mode for the kth slot can be determined as follows:

in summary, the available system optimization algorithm is shown as algorithm 1.

The system optimization algorithm based on the Lyapunov optimization theory comprises the following steps:

1) Initialization: k =1;

2)while TRUE；

3) Obtaining system channel state information CSI of a kth time slot, and reading energy state information B (k) of an IRS battery and user task queue state information Q (k);

4) Solving optimization problems (21), (23) and (30) corresponding to the three modes to obtain optimal solutions of d (k), l (k), t (k) and theta (k), and calculating Y _m (k)；

5) Determining system working mode m ^* (k)；

6) According to m ^* (k) Performing optimal resource allocation according to optimal solutions of d (k), l (k), t (k) and theta (k) in the corresponding system working mode, and updating queue states B (k + 1) and Q (k + 1) of the next time slot according to equations (8) and (10);

7)k＝k+1；

8)end while。

FIG. 3 shows the transmit power when the HAP is active (i.e., P) _A ) When varied, the power consumption performance of the scheme presented herein and the four baseline schemes varied. As can be seen from fig. 3, the proposed solution has the lowest energy consumption compared to the four reference solutions. Specifically, theIn other words, compared to the short-view solution, the energy consumption of the system of the solution proposed herein is only 10% -50% of the energy consumption; and saves more energy than the local and HAP-only computing schemes. Therefore, using the new protocol and system optimization algorithm proposed herein, significant savings in energy consumption on the user side can be achieved. Furthermore, it can be seen that when P is compared to the no IRS assistance scheme _A Smaller (e.g. P) _A =10 dBm), the proposed solution is substantially the same as its energy consumption performance, since in this case the IRS takes most of the time to collect energy to support its work, so that the role of the IRS in offloading tasks on the secondary user side is small. However, when P is _A The energy consumption of the proposed scheme is only 22.66% of that of the IRS-assisted-free scheme when =30dBm, thus demonstrating that deployment of IRS in the system can significantly reduce energy consumption of the user terminal.

Fig. 4 plots the effect of channel quality of a UA link on the energy consumption performance of different schemes. As can be seen from fig. 4, for the scheme proposed herein, the IRS-less-assistance scheme, the short-time scheme, and the HAP-only calculation scheme, since the task offloading is adopted, the energy consumption thereof increases as the UA link path loss exponent increases. In particular, when the path loss exponent is increased from 2.5 to 5, the energy consumption of the no IRS assistance scheme is increased by about 22 times, while the energy consumption of the scheme proposed herein is increased by only about 2 times, thereby further verifying that deploying IRS in the system can significantly save the energy consumption of the user side. Meanwhile, for the HAP-only calculation scheme, when the path loss exponent is increased from 2.5 to 5, the consumed energy is increased by about 6 times, thereby verifying that the energy consumption of the user terminal can be saved by using a partial offloading mode. Furthermore, the energy consumption performance of the proposed scheme is also significantly better than that of the short-view scheme for all UA link path loss indexes, thus further verifying that better energy consumption performance can be obtained using the new protocol and optimization algorithm proposed herein than the energy and task scheduling approach of documents [2-3 ].

Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (7)

1. A method for optimizing energy and task scheduling of an edge computing system is characterized by comprising the following steps:

the first step is as follows: based on a new energy and task scheduling protocol, the MEC system can be switched in an energy collection mode, an IRS auxiliary task unloading mode and an IRS standby task unloading mode in a self-adaptive manner according to the channel condition, the energy state of the IRS battery and the user task queue state;

the second step is that: modeling a system optimization problem based on the developed protocol, and minimizing long-term task unloading and energy consumption calculation of a user;

the third step: the method is characterized in that a Lyapunov optimization method is utilized to decompose the Lyapunov optimization method into a deterministic optimization problem based on time slots, and a convex optimization theory is utilized to solve the corresponding deterministic optimization problem.

2. The method of claim 1, wherein the method comprises the following steps: the specific steps in the first step are as follows:

s1: establishing a channel model;

taking a channel in an MEC system as a quasi-static channel;

the user side can unload the calculation task data to the HAP through the UA link and the URA link;

UA link, the channel coefficient in time slot k is denoted as h _UA (k) And modeling it as Rayleigh fading, i.e.

Where ρ is ₀ Is a reference distance d ₀ Path loss at =1m, α _UA Is the corresponding path loss exponent, d, of the UA channel link _UA Is the distance between the user terminal and the HAP,

is a complex gaussian random scattering component of zero mean and unit variance;

URA links including two channel links of user end to IRS (UR, user-to-IRS) and IRS to HAP (RA, IRS-to-HAP), wherein channel coefficient vectors in time slot k are uniformly expressed as

Wherein ab ∈ { UR, RA }, alpha _ab Is the channel path loss exponent from node a to node b, d _ab Is the distance between node a and node b, ζ _ab Is the rice factor associated with small scale fading,

is the ULA array response vector and,

is a complex matrix of I rows and J columns in

Middle diameter phi _ab (k) Expressed as angle of arrival or angle of departure of the respective signal, (. Cndot.) ^T As indicated by the operation of the transpose,

is a non-direct component in a rice fading channel, each element of which is a random scattering component of zero mean and unit variance;

is provided with

Represents the reflection vector of IRS in slot k, where θ _n (k) Is the phase shift of the nth reflecting element, for each reflectionThe reflection amplitude coefficients of the cells are all set to a maximum value that can be reached to maximize the signal reflected power, whereby the reflection coefficient of the IRS should satisfy the following constraint:

s2: the wireless power supply IRS assists the task unloading protocol;

the MEC system under the new protocol can be operated in an energy collection mode, an IRS auxiliary task unloading mode and an IRS standby task unloading mode, wherein t _e (k) And t _o (k) In the three modes, users can locally execute part of calculation tasks within the duration of the whole time slot, and the calculation task unloading of the users and the energy collection of the IRS can not be carried out simultaneously;

at slot k, the following equation holds: phi is a _I (k)t _e (k)+φ _II (k)(t _e (k)+t _o (k))+φ _III (k)t _o (k)＝T。

3. The method of claim 2, wherein the method comprises the following steps: in the energy collection mode, all time in one time slot is used for the energy collection of the IRS, in this case, the HAP transmits RF energy signals to the IRS, and the IRS collects energy from the RF energy signals, in this mode, the user side does not unload the calculation task data to the HAP, and only relies on the user side to locally execute the calculation task;

in an IRS auxiliary task unloading mode, dividing a time slot into two stages, and in the first stage, the IRS collects energy; in the second stage, the ue offloads the task data to the HAP with the assistance of the IRS, as a specific example, in this mode, when the initial energy of the IRS is sufficient, the first stage may not exist, and the IRS offloads the task data to the HAP at the time of the whole timeslot, that is, t is _e =0 and t _o ＝T；

In the IRS standby task offload mode, the user only offloads the computing task data to the HAP through the UA link, and the IRS is in a standby state with power off, which is selected in the following two cases: firstly, when the battery energy of the IRS is insufficient, the IRS can not participate in auxiliary task unloading, and secondly, when the channel quality of the UA link of the current time slot is good, a user can directly unload the calculation task to the HAP through the UA link.

4. The method of claim 1, wherein the method comprises the following steps: the second step comprises the following specific steps:

s1: the energy consumption model of the user comprises energy consumption of task unloading and energy consumption of task local calculation;

s2: an IRS energy collection and consumption model;

the IRS collects energy from the RF energy signal transmitted by the HAP in an energy collection mode and an IRS-assisted task offloading mode, and the energy collected by the IRS in slot k can be expressed as

In IRS-assisted task offloading mode, the energy consumed by the available IRS in slot k is E _C (k)＝μNφ _II (k)t _o (k)。

5. The method of claim 4, wherein the method comprises: the energy consumption of task unloading comprises the following steps:

when the system operates in the IRS auxiliary task unloading mode, the maximum achievable data transmission rate is as follows:

b is the bandwidth of the system, p (k) is the transmit power of the user terminal, σ ² At HAPAdditive white gaussian noise power. Let d (k) be t _o (k) The amount of task data offloaded during;

the energy consumption of the user side for executing task unloading is as follows:

when the IRS operates in the standby task unloading mode, the energy consumed by the user side for unloading the d (k) task data volume is energy;

s3: and problem modeling is carried out, and when a user side processes a computing task, the computing task amount in the task queue can be scheduled in a time period. When a time slot k begins, a user task queue state is represented as Q (k), at the end of the time slot k or equivalent time instant (k + 1), the user task queue state is represented as Q (k + 1), a user performs local calculation in three modes, task unloading is performed in an IRS auxiliary task unloading mode and an IRS standby task unloading mode, and D (k) is the amount of task data of a user side which performs and unloads locally in the time slot k, so that the user side has the task data

6. The method of claim 1, wherein the method for optimizing energy and task scheduling of the edge computing system comprises: the third step comprises the following specific steps:

s1: defining a virtual energy state based on the energy state B (k) of the IRS battery:

X(k)＝B(k)-G；

s2: where G =2TN μ is a time-independent constant described as:

X(k+1)＝X(k)+E _H (k)-E _C (k)；

s3: defining a quadratic lyapunov function as:

s4: introducing a Lyapunov drift function delta (omega (k)):

s5: further defining a Lyapunov drift penalty function obtained by weighting the Lyapunov drift function and the objective function of the deterministic optimization problem:

wherein λ is a non-negative weighting factor;

s6: theorem upper bound on lyapunov drift penalty function:

m is a finite constant independent of λ;

s7: the optimization target is rewritten from the target function of the problem into a Lyapunov drift penalty function, and the original problem can be converted into a problem for solving the minimum value of the upper bound by utilizing the upper bound of the drift penalty function:

d(k)≥0,l(k)≥0，T≥τ(k)≥0；

s8: determining an optimal system working mode based on a problem solving and system optimizing algorithm so as to obtain an optimal solution of the problem with the minimum value;

when phi is _I (k) When =1, the system operates in energy collection mode, and the problem of the minimum value can be abbreviated as:

s.t.l(k)≥0，

the objective function is O (k), equation

Solving, and combining a constraint condition l (k) to be more than or equal to 0 to obtain the optimal solution of the optimization variable l (k);

when phi is _II (k) With =1, the system is operating in IRS-assisted task offload mode, let Ψ' (k) = { d (k), l (k), t (k), Θ (k) }, then the problem of the minimum value can be rewritten as:

d(k)≥0,l(k)≥0，T≥τ(k)≥0；

s9: due to the fact that

The optimal solution for the optimization variable Θ (k) can thus be found as:

wherein

In obtaining l ^* (k) And theta ^* (k) Then, the following problem can be simplified:

s.t.d(k)≥0,T≥τ(k)≥0；

s10, solving the problems to obtain an optimal solution, and determining Y _m (k) (m ∈ { I, II, III }) so that the optimal system operating mode for the kth slot can be determined as follows:

7. the method of claim 6, wherein the method comprises: the system optimization algorithm comprises the following steps:

s1: initialization: k =1;

S2：while TRUE；

s3: obtaining system channel state information CSI of a kth time slot, and reading energy state information B (k) of an IRS battery and user task queue state information Q (k);

s4: solving the optimization problems corresponding to the three modes to obtain the optimal solution of d (k), l (k), t (k) and theta (k), and calculating Y _m (k)；

S5: determining system working mode m ^* (k)；

S6: according to m ^* (k) And the optimal solution of d (k), l (k), t (k) and theta (k) in the corresponding system working mode, performing optimal resource allocation, and updating queue states B (k + 1) and Q (k + 1) of the next time slot;

S7：k＝k+1；

S8：end while。

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