We study optimal admission of arriving customers to a Markovian finite-capacity queue, e.g. M/M/c/N queue, with several customer types. The system managers are paid for serving customers and penalized for rejecting them. The rewards and penalties depend on customer types. The penalties are modelled by a K-dimensional cost vector, K ≥ 1. The goal is to maximize the average rewards per unit time ...

In this paper, we consider a discrete time queueing system fed by a superposition of an ON and OFF source with heavy tail ON periods and geometric OFF periods and a D-BMAP (Discrete Batch Markovian Arrival Process). We study the tail behavior of the queue length distribution and both infinite and finite buffer systems are considered. In the infinite buffer case, we show that the asymptotic tail...

We consider the well-studied MMPP/PH/1 queue and illustrate a method to find an almost equivalent model, the MTCP/PH/1. MTCP stands for Markovian TransitionCounting Process. It is a counting process that has similar characteristics to MMPP (Markov Modulated Poisson Process). We prove that for a class of MMPPs there is an equivalent class of MTCPs. We then use this property to suggest an approxi...

the stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use markovian jumps to model stochastic reaction diffusion systems‎. ‎in this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with markovian jumps‎. ‎under some reasonable conditions‎, ‎we show that the trivial solution of stocha...

Abstract: We consider a finite-buffer single server queue with single (multiple) vacation(s) under batch Markovian Arrival Process (BMAP). The service discipline is varying number limited service, also called E-limited with limit variation (ELV) where the server serves until either the system is emptied or a randomly chosen limit of l customers have been served. Queue length distributions at va...

In this paper, we investigate the response time of a multi-server processor sharing (PS) model. A multi-server PS model is a PS queue but the number of requests which can be processed simultaneously is limited by a threshold. An arriving request has to wait in the queue if the number of requests exceeds the threshold. Assuming Markovian arrival input of requests and general processing time dist...

We consider an infinite-buffer single-server queue where inter-arrival times are phase-type (PH), the service is provided according to Markovian service process (MSP ), and the server may take single, exponentially distributed vacations when the queue is empty. The proposed analysis is based on roots of the associated characteristic equation of the vector-generating function (VGF) of system-len...

We consider a finite-buffer single server queueing system with queue-length dependent vacations where arrivals occur according to a batch Markovian arrival process (BMAP). The service discipline is P-limited service, also called E-limited with limit variation (ELV) where the server serves until either the system is emptied or a randomly chosen limit of L customers has been served. Depending on ...

We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss networks. We use a variation of Dominated Coupling From The Past for which we simulate a stationary infinite server queue backwards in time and analyze the running time in heavy traffic. In particular, we are able to simulate stationary renewal marke...