Queuing Theory Based Modeling And Performance Analysis Of Delay Variation Of Communication Network

With the rapid development of IoT (Internet of Things), M2M services (Machine toMachine, Man to Machine, Machine to Mobile network) have found an increasingly wideutilization in all fields. Heterogeneous M2M services from various IoT applications will sharethe current communication network with the traditional H2H (Human to Human) servicessimultaneously. According to the feature of delay tolerance, services in the network areroughly divided into two classes, the real-time services and non real-time services. For thereal-time services, including H2H voice, and H2H video, delay variation remains the vitalparameter of QoS. The characteristics of M2M services are different from the existing H2Hservices, therefore, when huge amounts of M2M services want to access into existing andfuture communication network, will certainly bring considerable impacts on delay variationperformance of the real-time services. Researching on delay variation performance of thecommunication network bearing mixed services, and exploring the impacts of non real-timeservices on delay variation performance of real-time services, is an essential step to evaluatethe performance of communication network and optimize the QoS of real-time services.As a mathematical tool based on stochastic process theory, queuing theory is often usedto model the communication network and evaluate its performance. In this paper, thereal-time services are considered as tagged stream, and the non real-time services areconsidered as background stream. We research the delay variation performance of thecommunication network based on tandem queuing theory. We propose two different methodsto solve delay variation in the given queuing systems, and investigate the factors which mayaffect the delay variation performance from different aspects. Our work and contribution issummarized as follows.First, this paper proposes a steady-state analysis method to solve the delay variation ofthe tandem queuing system. The heterogeneous MMBP-2source models are used to depictthe arrival processes of the real-time and non real-time services respectively. And the entirenetwork is modeled as a discrete time queuing system N MMBP-2F+MMBP-2B/Geo/1(K). Bymapping the services process of the non real-time services into the services time of thereal-time services, the queuing model MMBP-2F+MMBP-2B/Geo/1(K) is equivalent toMMBP-2F/Geff/1(K). Based on birth and death process, a two-dimensional markov chain isimplemented to describe the steady-states transition of the system, and then the stationary delay distribution and delay variation in single node are obtained. In the process of solving theend to end delay variation, by analyzing the departure process and using the parameter fittingmethods, we firstly calculate delay variation in each node by assuming nodes in the tandemmodel are independent of each other. Then we research the correlation in tandem queues, andobtain the actual end to end delay variation. Some simulation results show that delayincreases as the load increases, however, delay variation decreases with the increasing load.Moreover, lots of simulation results show that delay variation and delay present differentfeatures in traffic burstiness, correlation and the network congestion. These conclusions willprovide theoretical basis for QoS optimization of real-time services.Considering that when the arrival processes of the real-time and non real-time servicesare both general discrete time stochastic processes in the real communication network, it’sdifficult to obtain the system steady-states transition probability, therefore the method basedon steady-state analysis is not suitable any more. Hence, this paper proposes a transient-statequeuing analysis method to solve delay variation. A discrete time renewal and a batch arrivalprocess are used to model the arrival processes of real-time services and non real-timeservices respectively, and the network is modeled as N DAP+D-BAP/D/1tandem queuingsystem. In the DAP+D-BAP/D/1queuing model, the delay variation is equivalent to theevolution of the queue length in the time between arrivals of the real-time services. Therefore,we first analyze the transient course of the queuing model in terms of both the queue lengthand the time between arrivals of the real-time services, and obtain the stationary queue lengthdistribution. And on this basis, we derive the probability distribution function of the delay anddelay variation in two cases where real-time services are served at random order and at firstorder respectively when they are arriving in the same slot with the non real-time services. Inparticular we analyze the distribution of the time between two successive departures. Byapproximating the output of the real-time services with a renewal stream and applying this asthe input to the next node, by applying the queuing model recursively, we get an end to enddelay description and the evolution of the delay variation. Finally, we choose thecomplementary cumulative distribution function and the probability distribution function asthe performance indicators of delay and delay variation, and we investigate the effects oftraffic load and service order on delay and delay variation performance in the case where thereal-time services are deterministic and the non real-time services are modeled as possionstream.