We present an analysis of the number of losses, caused by the buffer overflows, in a finite-buffer queue with batch arrivals and autocorrelated interarrival times. Using the batchMarkovian arrival process, the formulas for the average number of losses in a finite time interval and the stationary loss ratio are shown. In addition, several numerical examples are presented, including illustrations...

The delay analysis of a statistical multiplexer with heterogeneous input sources is presented in this work. The traac generated by an individual source is described in terms of a discrete-time Batch Markovian arrival process with geometrically distributed idle periods. An exact closed form expression for the mean packet delay in the system is obtained by exploiting the stochastic structure of t...

The transient analysis of a queuing system with fixed-size batch Poisson arrivals and a single server with exponential service times is presented. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. These functions are shown to be a generalization of the modified Bessel functions of the first kind, with the batch siz...

To make comprehensive and objective analysis of the performance of the cloud computing system center, a cloud computing center system analysis model based on queuing theory is proposed. First, to describe the characteristics of user’s service changes request arrived at center by using Poisson distribution, the batch arrival system model was established based on queuing theory, then solve the st...

Many performance models for interconnection networks in parallel computing systems have been reported under the assumption of non-bursty Poisson arrival process. However, network traffic loads often exhibit bursty nature, which can markedly degrade the system performance. In order to develop a cost-efficient performance evaluation tool, this paper proposes a new analytical model for torus netwo...

This paper develops a finite-capacity single-vacation queueing model with close-down/setup times and batch Markovian arrival process (BMAP) for the statistic behavior of the typical ARQ schemes (Stop-and-Wait, Go-Back-N, Selective Repeat) at transmitter buffer. We obtain the queue length distribution, the average waiting time of arbitrary data frame and the server utilization ratio of the trans...

We consider a single batch machine on-line scheduling problem with jobs arriving over time. A batch processing machine can handle up to B jobs simultaneously as a batch, and the processing time for a batch is equal to the longest processing time among the jobs in it. Each job becomes available at its arrival time, which is not known in advance, and its characteristics, such as processing time a...

1. The MM ∑K k=1 CPPk/GE/c/L G-Queue It is well known that the traffic in today’s telecommunication systems often exhibits burstiness i.e. batches of transmission units (e.g. packets) arrive together with correlation among the interarrival times [12]. Several models have been proposed to model such arrival-service processes, queues and networks. These include the compound Poisson process (CPP) ...

We develop approximate solutions for the equilibrium queue length probability distribution of queues in open Markovian networks by considering each queue independently, constructing its arrival process as the join of each contributing queue's departing traffic. Without modulation and non-unit batches, we would only need to consider mean internal traffic rates, modelling each queue as M/M/1 to g...

Consider a continuous-time queueing network with probabilistic routing, including feedback. External batch arrival and batch service processes are characterized by independent Markov additive processes (MAPs). An effective change of measure is proposed for use in importance sampling procedure to estimate the probability of buffer overflow in an arbitrary (‘target’) queue during its busy period....