In this paper, we identify the batch Markovian arrival process (BMAP) as analytically tractable model of choice for aggregated traffic modeling of IP networks. The key idea of this aggregated traffic model lies in customizing the batch Markovian arrival process such that the different lengths of IP packets are represented by rewards (i.e., batch sizes of arrivals) of the BMAP. The utilization o...

The authors analyse a discrete-time based finite queueing model with deterministic service times and a Markov modulated batch Bernoulli process (MMBBP) as a bursty input traffic model in order to investigate the performance of a double threshold based dynamic bandwidth allocation scheme for IP traffic on ATM networks. It is assumed that the segmentation processing time devoted to each cell requ...

 System occupancy of a two-class batch-service queue with class-dependent variable server capacity Jens Baetens, Bart Steyaert, Dieter Claeys and Herwig Bruneel  Sojourn time analysis for processor sharing loss system with unreliable server Konstantin Samouylov, Valery Naumov, Eduard Sopin, Irina Gudkova and Sergey Shorgin  A law of large numbers for M/M/c/Delayoff-Setup queues with nonstati...

We derive convexity results and related properties for the value functions of tandem queueing systems. The results for standard multi-server queues are new. For completeness we also prove and generalize existing results on tandems of controllable queues. The results can be used to compare queueing systems. This is done for systems with and without batch arrivals, and for systems with different ...

We consider finiteand infinite-capacity queues with discrete-time batch Markovian arrival processes (D-BMAP) under the assumption of the Late Arrival System with Delayed Access as well as the Early Arrival System. Using simple arguments such as the balance equation, “rate in = rate out,” we derive relationships among the stationary queue lengths at arrival, at departure, and at random epochs. S...

Many systems of real word are modeled by retrial queuing system with batch arrivals. Analytical formulas for this class of systems are complicated and address only particular cases. The paper presents a study approach for this kind of systems, based on discrete event simulation. It is shown that the given algorithm has a polynomial complexity. Also, the object-oriented design we used for implem...

Throughout this internship report, polling systems play a central role. Polling systems are queueing systems consisting of multiple queues, attended by a single server. The server can only serve one queue at a time. Whenever the server moves from one queue to another, a stochastic, non-zero switch-over time is incurred. The server never idles; even when there are no customers waiting in the who...

Response time density is obtained in a tandem pair of Markovian queues with both batch arrivals and departures. The method uses conditional forward reversed node sojourn times derives the Laplace transform response probability function case that sizes are finite. result derived by generating takes into account path not overtake-free sense tagged task being tracked affected later at second queue...

Hysteretic control of arrivals is one of the most easy-to-implement and effective solutions of overload problems occurring in SIP-servers. A mathematical model of an SIP server based on the queueing system M [X]|G|1〈L,H〉|〈H,R〉 with batch arrivals and two hysteretic loops is being analyzed. This paper proposes two analytical methods for studying performance characteristics related to the number ...