切换服务网络的稳定性及交通信号控制应用
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摘要
切换服务网络是一类复杂的网络系统，可以用来建模一类具有公共资源使用冲突的物质或信息流系统，典型的例子包括交通信号控制系统。论文从交通信号控制实际问题出发，针对切换服务网络系统，从两个方面展开研究：针对单机切换服务系统，提出新的服务器调度策略；针对多机切换服务网络系统，提出一般的网络模型，并以城市交通网络信号控制为实例，提出新的信号控制策略。主要研究成果总结如下。
针对单机切换服务系统，当服务器每次只为一个缓冲器服务时，论文首先提出了两类服务器调度策略，即“固定顺序清空切换”调度策略和“优先服务等待时间最长的缓冲器”调度策略。在满足“缓冲器总负荷小于1”的条件下，证明了两类调度策略下切换服务系统是周期稳定的，获得了稳定周期解的解析表达式。服务器“优先服务等待时间最长的缓冲器”调度策略可优化服务器切换服务顺序，使得缓冲器等待服务时间(或未被服务时间)最小。同时，建立了切换服务系统服务器调度策略与交叉口信号控制之间的等价关系，从而将两类服务器调度策略直接应用于信号交叉口的稳态控制。
其次，考虑缓冲器有服务时间约束的服务器调度策略的设计问题，推广了服务器“固定顺序清空切换”调度策略。首先提出了服务器“带服务时间上限”调度策略，服务器在该调度策略下分配给每个缓冲器一个服务时间上限，以保证缓冲器内工作量较大时各个缓冲器可以公平地得到服务。证明了在满足“缓冲器总负荷小于各缓冲器的服务时间上限调整因子的最小值与最大值之比”的条件下，切换服务系统在服务器“带服务时间上限”调度策略下是周期稳定的。由于交叉口信号控制通常要考虑最短及最长信号相位绿时约束，相当于每个缓冲器同时满足最短及最长服务时间约束。论文进一步提出了服务器“带服务时间上下限”调度策略，证明了当缓冲器总负荷满足条件“小于各缓冲器的服务时间下限调整因子的最小值与最大值之比，且小于各缓冲器的服务时间上限调整因子的最小值与最大值之比”时，切换服务系统在服务器“带服务时间上下限”调度策略下是周期稳定的。由于对于大部分实际问题，缓冲器内的容量(即缓冲器内能容纳的最大工作量)是有限的，因此在服务器“带服务时间上下限”调度策略的基础上，当缓冲器的容量有限时，给出了可行初始状态的检测条件，即服务器在第1个切换周期内未破坏缓冲器容量约束的切换服务系统的解所对应的初始状态。
第三，进一步考虑服务器每次可同时为多个缓冲器服务情况下的切换服务系统服务器调度策略设计。同时被服务的缓冲器集合称为一个相位，类似于信号交叉口包含多支受控车流的信号相位。论文提出了服务器“带相位服务时间上下限”调度策略，该策略为上述服务器“带服务时间上下限”调度策略的进一步推广。证明了当关键缓冲器总负荷满足条件“小于各相位的服务时间下限调整因子的最小值与最大值之比，且小于各相位的服务时间上限调整因子的最小值与最大值之比”时，切换服务系统在服务器“带相位服务时间上下限”调度策略下是周期稳定的。从而该服务器调度策略可应用于更一般的信号交叉口稳态控制。
针对多机服务网络，论文提出了一个一般的网络模型，称为动态图混杂系统。城市交通网络是一类特殊的多机服务网络系统，论文以交通网络信号控制设计为实例，提出了新的信号控制方法。首先采用有向动态图建模网络拓扑结构，并采用元胞传输模型建模路段间交通流的转移关系。若假定网络模型采样周期为网络公共信号周期，则得到交通网络信号控制模型，该模型为一类离散时间线性时不变控制系统，其中系统的状态变量为路段相对占有率，系统的状态矩阵为单位矩阵。网络状态一致性(或均衡性)是一个重要的性能指标。对于交通网络信号控制模型，论文考虑了以网络状态可达到渐近稳定一致为控制目标的状态反馈控制律设计。
针对更加一般的情况，以系统状态可达到渐近稳定一致为控制目标，考虑连续时间及离散时间线性时不变控制系统控制器的设计问题。对于连续时间情况，假定系统的状态矩阵的行和均为0；而对于离散时间情况，假定系统的状态矩阵的行和均为1。由于一致性问题可转化为平衡点集的稳定性问题，论文借助于部分变量稳定性理论的相关结果和工具，采用线性矩阵不等式方法求解状态反馈控制律的反馈增益矩阵。
Switched server network is a class of complex networked systems, which canmodel systems with conflicting material or information flows accessing commonresources, e.g., traffic signal control system. From practical problems in traffic signalcontrol, this paper conducts research for switched server network in two aspects. First,new scheduling policies of the server are proposed for switched server system withone server. Furthermore, more general network model is proposed for multiple servernetwork system, and then signal control of urban traffic network is taken as a typicalexample, for which new signal control strategy is presented. Main research results aresummarized as follows.
For switched server system, under the case that the server serves only one buffereach time, two classes of scheduling policies of the server are first presented, i.e., thescheduling policy “emptying and switching in a fixed order” and the schedulingpolicy “priority to the buffer with longest waiting time”, under which switched serversystem is periodically stable if the total load of buffers is less than one. In addition,the analytical expression of stable periodic solution to the system can be obtained.The scheduling policy “priority to the buffer with longest waiting time” can optimizeswitching sequence of the server, such that the waitting service time (or un-servedtime) of buffers is minimized. Moreover, the equivalent relation between thescheduling policy of the server for switched server system and the signal control forsignalized intersections, is established. Then, two classes of scheduling policies of theserver can be directly applied to steady-state control of signalized intersections.
Furthermore, this paper generalizes the scheduling policy “emptying andswitching in a fixed order”, and considers the design problem of scheduling policiesof the server with service-time limit of buffers. The scheduling policy “maximumservice-time limit” is first proposed, under which the server assigns a maximumservice-time limit to each buffer, such that each buffer can be fairly served in the caseof large workload in the buffer. It is proved that switched server system under thescheduling policy “maximum service-time limit” is periodically stable if the total loadof buffers is less than the ratio of the minimum and the maximum of maximumservice-time limit adjustment factors of buffers. However, the minimum and themaximum green time durations of each of signal phases should be considered forsignal control of signalized intersections, which corresponds to the case that eachbuffer simultaneously satisfies the minimum and the maximum service-time limit.Thus, the scheduling policy “maximum and minimum service-time limit” is proposed,under which switched server system is periodically stable if the total load of buffers is less than the ratio of the minimum and the maximum of minimum service-time limitadjustment factors of buffers, as well as the ratio of the minimum and the maximumof maximum service-time limit adjustment factors of buffers. For most of real-worldproblems, the buffer capacity (i.e., the maximum workload the buffer canaccommodate) is finite. Based on the scheduling policy “maximum and minimumservice-time limit”, the checking condition for feasible initial states is presented in thecase of finite buffer capacity, i.e., the initial state such that the solution to switchedserver system does not violate buffer capacity constraints within first cyclic switchingof the server.
Third, the scheduling policies of the server are designed for switched serversystem with the server simultaneously serving multiple buffers each time. The subsetof simultaneously served buffers is called a phase, similar to a signal phase containingmultiple controlled vehicle flows in a signalized intersection. This paper proposes thescheduling policy “maximum and minimum phase service-time limit”, which isfurther generalization of the scheduling policy “maximum and minimum service-timelimit”. It is proved that switched server system under the scheduling policy“maximum and minimum phase service-time limit” is periodically stable if the totalload of critical buffers is less than the ratio of the minimum and the maximum ofminimum service-time limit adjustment factors of phases, as well as the ratio of theminimum and the maximum of maximum service-time limit adjustment factors ofphases. Then, the proposed scheduling policy can be applied to steady-state control ofmore general type of signalized intersections.
For multiple server networks, a general network model is presented, called“Dynamic Graph Hybrid System”. Signal control design of traffic network is taken asa practical example, which is a special class of multiple server networks, and thennew signal control method is proposed. The topological structure of traffic network ismodeled by directed dynamic graph, and the transition of vehicle flows between roadsections is modeled by cell transmission model. Under the assumption that thesampled period of the model is equal to common signal period of traffic network, thesignal control model of traffic network can be obtained, which is a discrete-time lineartime-invariant control system with state varibles being relative occupancy of roadsections and state matrix being unit matrix. The consensus (or balance) of states of thenetwork is an important performance index. For the signal control model of trafficnetwork, the state-feedback control law is designed such that the closed-loop systemcan reach asymptotic stable consensus.
For more general case, taking asymptotic stable consensus of the system ascontrol objective, this paper presents methods for the design of the state-feedbackcontrol law for continuous-time and discrete-time linear time-invariant control systemrespectively. The row sums of state matrix of the system are assumed equal to zero for the continuous-time case, and one for the discrete-time case. In fact, the problem ofstate consensus of the system can be transformed to the problem of stability of theequilibrium set of the system. Thus, linear matrix inequality method can be applied tonumerically solve feedback gain matrix of the state-feedback control law by usingpartial stability theory.
针对单机切换服务系统，当服务器每次只为一个缓冲器服务时，论文首先提出了两类服务器调度策略，即“固定顺序清空切换”调度策略和“优先服务等待时间最长的缓冲器”调度策略。在满足“缓冲器总负荷小于1”的条件下，证明了两类调度策略下切换服务系统是周期稳定的，获得了稳定周期解的解析表达式。服务器“优先服务等待时间最长的缓冲器”调度策略可优化服务器切换服务顺序，使得缓冲器等待服务时间(或未被服务时间)最小。同时，建立了切换服务系统服务器调度策略与交叉口信号控制之间的等价关系，从而将两类服务器调度策略直接应用于信号交叉口的稳态控制。
其次，考虑缓冲器有服务时间约束的服务器调度策略的设计问题，推广了服务器“固定顺序清空切换”调度策略。首先提出了服务器“带服务时间上限”调度策略，服务器在该调度策略下分配给每个缓冲器一个服务时间上限，以保证缓冲器内工作量较大时各个缓冲器可以公平地得到服务。证明了在满足“缓冲器总负荷小于各缓冲器的服务时间上限调整因子的最小值与最大值之比”的条件下，切换服务系统在服务器“带服务时间上限”调度策略下是周期稳定的。由于交叉口信号控制通常要考虑最短及最长信号相位绿时约束，相当于每个缓冲器同时满足最短及最长服务时间约束。论文进一步提出了服务器“带服务时间上下限”调度策略，证明了当缓冲器总负荷满足条件“小于各缓冲器的服务时间下限调整因子的最小值与最大值之比，且小于各缓冲器的服务时间上限调整因子的最小值与最大值之比”时，切换服务系统在服务器“带服务时间上下限”调度策略下是周期稳定的。由于对于大部分实际问题，缓冲器内的容量(即缓冲器内能容纳的最大工作量)是有限的，因此在服务器“带服务时间上下限”调度策略的基础上，当缓冲器的容量有限时，给出了可行初始状态的检测条件，即服务器在第1个切换周期内未破坏缓冲器容量约束的切换服务系统的解所对应的初始状态。
第三，进一步考虑服务器每次可同时为多个缓冲器服务情况下的切换服务系统服务器调度策略设计。同时被服务的缓冲器集合称为一个相位，类似于信号交叉口包含多支受控车流的信号相位。论文提出了服务器“带相位服务时间上下限”调度策略，该策略为上述服务器“带服务时间上下限”调度策略的进一步推广。证明了当关键缓冲器总负荷满足条件“小于各相位的服务时间下限调整因子的最小值与最大值之比，且小于各相位的服务时间上限调整因子的最小值与最大值之比”时，切换服务系统在服务器“带相位服务时间上下限”调度策略下是周期稳定的。从而该服务器调度策略可应用于更一般的信号交叉口稳态控制。
针对多机服务网络，论文提出了一个一般的网络模型，称为动态图混杂系统。城市交通网络是一类特殊的多机服务网络系统，论文以交通网络信号控制设计为实例，提出了新的信号控制方法。首先采用有向动态图建模网络拓扑结构，并采用元胞传输模型建模路段间交通流的转移关系。若假定网络模型采样周期为网络公共信号周期，则得到交通网络信号控制模型，该模型为一类离散时间线性时不变控制系统，其中系统的状态变量为路段相对占有率，系统的状态矩阵为单位矩阵。网络状态一致性(或均衡性)是一个重要的性能指标。对于交通网络信号控制模型，论文考虑了以网络状态可达到渐近稳定一致为控制目标的状态反馈控制律设计。
针对更加一般的情况，以系统状态可达到渐近稳定一致为控制目标，考虑连续时间及离散时间线性时不变控制系统控制器的设计问题。对于连续时间情况，假定系统的状态矩阵的行和均为0；而对于离散时间情况，假定系统的状态矩阵的行和均为1。由于一致性问题可转化为平衡点集的稳定性问题，论文借助于部分变量稳定性理论的相关结果和工具，采用线性矩阵不等式方法求解状态反馈控制律的反馈增益矩阵。
Switched server network is a class of complex networked systems, which canmodel systems with conflicting material or information flows accessing commonresources, e.g., traffic signal control system. From practical problems in traffic signalcontrol, this paper conducts research for switched server network in two aspects. First,new scheduling policies of the server are proposed for switched server system withone server. Furthermore, more general network model is proposed for multiple servernetwork system, and then signal control of urban traffic network is taken as a typicalexample, for which new signal control strategy is presented. Main research results aresummarized as follows.
For switched server system, under the case that the server serves only one buffereach time, two classes of scheduling policies of the server are first presented, i.e., thescheduling policy “emptying and switching in a fixed order” and the schedulingpolicy “priority to the buffer with longest waiting time”, under which switched serversystem is periodically stable if the total load of buffers is less than one. In addition,the analytical expression of stable periodic solution to the system can be obtained.The scheduling policy “priority to the buffer with longest waiting time” can optimizeswitching sequence of the server, such that the waitting service time (or un-servedtime) of buffers is minimized. Moreover, the equivalent relation between thescheduling policy of the server for switched server system and the signal control forsignalized intersections, is established. Then, two classes of scheduling policies of theserver can be directly applied to steady-state control of signalized intersections.
Furthermore, this paper generalizes the scheduling policy “emptying andswitching in a fixed order”, and considers the design problem of scheduling policiesof the server with service-time limit of buffers. The scheduling policy “maximumservice-time limit” is first proposed, under which the server assigns a maximumservice-time limit to each buffer, such that each buffer can be fairly served in the caseof large workload in the buffer. It is proved that switched server system under thescheduling policy “maximum service-time limit” is periodically stable if the total loadof buffers is less than the ratio of the minimum and the maximum of maximumservice-time limit adjustment factors of buffers. However, the minimum and themaximum green time durations of each of signal phases should be considered forsignal control of signalized intersections, which corresponds to the case that eachbuffer simultaneously satisfies the minimum and the maximum service-time limit.Thus, the scheduling policy “maximum and minimum service-time limit” is proposed,under which switched server system is periodically stable if the total load of buffers is less than the ratio of the minimum and the maximum of minimum service-time limitadjustment factors of buffers, as well as the ratio of the minimum and the maximumof maximum service-time limit adjustment factors of buffers. For most of real-worldproblems, the buffer capacity (i.e., the maximum workload the buffer canaccommodate) is finite. Based on the scheduling policy “maximum and minimumservice-time limit”, the checking condition for feasible initial states is presented in thecase of finite buffer capacity, i.e., the initial state such that the solution to switchedserver system does not violate buffer capacity constraints within first cyclic switchingof the server.
Third, the scheduling policies of the server are designed for switched serversystem with the server simultaneously serving multiple buffers each time. The subsetof simultaneously served buffers is called a phase, similar to a signal phase containingmultiple controlled vehicle flows in a signalized intersection. This paper proposes thescheduling policy “maximum and minimum phase service-time limit”, which isfurther generalization of the scheduling policy “maximum and minimum service-timelimit”. It is proved that switched server system under the scheduling policy“maximum and minimum phase service-time limit” is periodically stable if the totalload of critical buffers is less than the ratio of the minimum and the maximum ofminimum service-time limit adjustment factors of phases, as well as the ratio of theminimum and the maximum of maximum service-time limit adjustment factors ofphases. Then, the proposed scheduling policy can be applied to steady-state control ofmore general type of signalized intersections.
For multiple server networks, a general network model is presented, called“Dynamic Graph Hybrid System”. Signal control design of traffic network is taken asa practical example, which is a special class of multiple server networks, and thennew signal control method is proposed. The topological structure of traffic network ismodeled by directed dynamic graph, and the transition of vehicle flows between roadsections is modeled by cell transmission model. Under the assumption that thesampled period of the model is equal to common signal period of traffic network, thesignal control model of traffic network can be obtained, which is a discrete-time lineartime-invariant control system with state varibles being relative occupancy of roadsections and state matrix being unit matrix. The consensus (or balance) of states of thenetwork is an important performance index. For the signal control model of trafficnetwork, the state-feedback control law is designed such that the closed-loop systemcan reach asymptotic stable consensus.
For more general case, taking asymptotic stable consensus of the system ascontrol objective, this paper presents methods for the design of the state-feedbackcontrol law for continuous-time and discrete-time linear time-invariant control systemrespectively. The row sums of state matrix of the system are assumed equal to zero for the continuous-time case, and one for the discrete-time case. In fact, the problem ofstate consensus of the system can be transformed to the problem of stability of theequilibrium set of the system. Thus, linear matrix inequality method can be applied tonumerically solve feedback gain matrix of the state-feedback control law by usingpartial stability theory.
引文
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