Modeling correlated traffic with a generalized IPP

Lee, Y. D.; Liefvoort, A. van de; Wallace, Victor L.

doi:10.1016/s0166-5316(99)00071-1

Cited by 15 publications

(3 citation statements)

References 20 publications

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“…Most of the researches on traffic modeling based on queuing theory use mathematical models to describe the arrival process of services for the sake of reducing the difficulties in solving queuing models [1][2] [3] . In the aspect of the solution of the G/M/1/K queuing model, Sunggon Kim derived the stationary distribution of the queue length of G/M/1/K model with two-stage service policy [4] .…”

Section: Introductionmentioning

confidence: 99%

Network Modeling and Performance Analysis under Time-Varying Channel and General Arrival of M2M Services

Fen

Zhang

et al. 2013

AMR

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To investigate and forecast the traffic characteristics of important M2M service--Small data service, we modeled its arrival process and analyzed the effects it has on current wireless network. By simulating service logic and designing traffic generation function of typical M2M small data service on network simulation platform (OPNET), we modeled packet inter-arrival time of M2M aggregate traffic with general distribution Gm. Considering the time-varying feature of wireless channel, MMPP-2 is used to model the service process of WLAN access network. Based on the queuing theory, we solve Gm/MMPP/1/K model under general arrival of M2M small data service and time-varying channel, then we obtained the performance metrics of the queuing system. The results indicate that (1) Hurst parameter of M2M aggregate traffic is approximately estimated as 0.7, (2) M2M small data service has the characteristics of delay-tolerance, as a result, system blocking rate can be effectively reduced by increasing the buffer size in the error-prone wireless environment, this solution is feasible.

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Section: Introductionmentioning

confidence: 99%

Network Modeling and Performance Analysis under Time-Varying Channel and General Arrival of M2M Services

Fen

Zhang

et al. 2013

AMR

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Section: Introductionmentioning

confidence: 99%

Network Modeling and Performance Analysis under Time-varying Channel and General Arrival of M2M Services

Fu¹,

Chi²,

Zhang³

et al. 2012

Proceedings of the 2012 2nd International Conference on Computer and Information Applications (ICCIA 2012)

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Abstract-Toinvestigate and forecast the traffic characteristics of important M2M service--Small data service, we modeled its arrival process and analyzed the effects it has on current wireless network. By simulating service logic and designing traffic generation function of typical M2M small data service on network simulation platform (OPNET), we modeled packet inter-arrival time of M2M aggregate traffic with general distribution Gm. Considering the time-varying feature of wireless channel, MMPP-2 is used to model the service process of WLAN access network. Based on the queuing theory, we solve Gm/MMPP/1/K model under general arrival of M2M small data service and time-varying channel, then we obtained the performance metrics of the queuing system. The results indicate that (1) Hurst parameter of M2M aggregate traffic is approximately estimated as 0.7, (2) M2M small data service has the characteristics of delay-tolerance, as a result, system blocking rate can be effectively reduced by increasing the buffer size in the error-prone wireless environment, this solution is feasible. Key words-M2M, small data service, traffic model, time-varying wireless channel. I INTRODUCTIONM2M service refers to all the services related to machine communications. The number of M2M devices is becoming trillion in the near future. Considering the characteristics of WLAN, such as high transmission rate, simple network topology and easy to deploy, it should act as the bearing network of M2M applications. Using the simulation platform, we analyze the flow characteristics of M2M services based on the behavior features of M2M devices and then establish the arrival model of M2M aggregated traffic. Queuing theory is used to investigate the system performance of M2M bearing network under time-varying channel. Moreover, we explore the method to reduce the blocking rate.Most of the researches on traffic modeling based on queuing theory use mathematical models to describe the arrival process of services for the sake of reducing the difficulties in solving queuing models. In the aspect of the solution of the G/M/1/K queuing model, Sunggon Kim derived the stationary distribution of the queue length of G/M/1/K model with two-stage service policy [4] . Some researches investigate relationship between M/G/1/K and G/M/1/K queuing systems [5] . To enhance the system performance, Jau-Chuan Ke considered the single vacation model G/M/1/K with N threshold policy [6] ; Mohsin Iftikhar solved the multi-class G/M/1 queuing system with self-similar input and non-preemptive priority [7] . However, all above researches about G/M/1/K queuing model focus on the theoretical analysis and mathematical solutions and there are few people paying close attention to the general arrival distribution of specific services in real networks; On the other hand, at present, the negative exponential distribution is widely used to model the network service time, but the time-varying characteristics of wireless channel makes it impossible to model the service process of wireless n...

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“…321-331], [17], [26], insurance risk [1, pp. 240-244], [5], renewal theory [2], [7], and telecommunications [16], [19], their usage is significantly less widespread than that of phasetype distributions. There are two main reasons for this.…”

Section: Introductionmentioning

confidence: 99%

An alternative characterization for matrix exponential distributions

Fackrell

2009

Adv. Appl. Probab.

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A necessary condition for a rational Laplace-Stieltjes transform to correspond to a matrix exponential distribution is that the pole of maximal real part is real and negative. Given a rational Laplace-Stieltjes transform with such a pole, we present a method to determine whether or not the numerator polynomial admits a transform that corresponds to a matrix exponential distribution. The method relies on the minimization of a continuous function of one variable over the nonnegative real numbers. Using this approach, we give an alternative characterization for all matrix exponential distributions of order three.

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Modeling correlated traffic with a generalized IPP

Cited by 15 publications

References 20 publications

Network Modeling and Performance Analysis under Time-Varying Channel and General Arrival of M2M Services

Network Modeling and Performance Analysis under Time-Varying Channel and General Arrival of M2M Services

Network Modeling and Performance Analysis under Time-varying Channel and General Arrival of M2M Services

An alternative characterization for matrix exponential distributions

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