In this paper, we consider a single server queueing system in which the arrivals occur according to Markovian arrival process (MAP). The served customers may be recruited (or opted from those customers’ point of view) act as secondary servers provide services waiting customers. Such who are referred servers. service times main well that assumed exponentially distributed possibly with different ...

We obtain the queue length probability distribution at equilibrium for a multi-server, single queue with generalised exponential (GE) service time distribution and a Markov modulated compound Poisson arrival process (MMCPP)—i.e. a Poisson point process with bulk arrivals having geometrically distributed batch size whose parameters are modulated by a Markovian arrival phase process. This arrival...

This paper presents a decision model that uses empirical Bayesian estimation to construct a server-dependent M/M/2/L queuing system. A Markovian queue with a number of servers depending upon queue length with finite capacity is discussed. This study uses the number of customers for initiating and turning off the second server as decision variables to formulate the expected cost minimization mod...

Motivated by an application in wireless random-access networks, we study a class of polling systems with Markovian routing, in which the server visits the queues in an order governed by a discrete-time Markov chain. Assuming that the service disciplines at each of the queues fall in the class of branching-type service disciplines, we derive a functional equation for (the probability generating ...

The finite capacity queues, G I / P H / 1 / N and PH/G/1 /N, in which customers are served in groups of varying sizes were recently introduced and studied in detail by the author. In this paper we consider a finite capacity queue in which arrivals are governed by a particular Markov renewal process, called a Markovian arrival process (MAP). With general service times and with the same type of s...

| In this paper we provide the analysis of a rate-based access control scheme in high speed environments based on a buuered leaky bucket algorithm. The analysis is carried out in discrete time which is representative of an ATM environment. For the cell arrivals to the leaky bucket we consider a general discrete Markovian arrival process which models bursty and modulated sources. The key of our ...

Traffic engineering of IP networks requires the characterization and modeling of network traffic on multiple time scales due to the existence of several statistical properties that are invariant across a range of time scales, such as selfsimilarity, LRD and multifractality. These properties have a significant impact on network performance and, therefore, traffic models must be able to incorpora...