The Markovian Arrival Process (MAP), which contains the Markov Modulated Poisson Process (MMPP) and the Phase-Type (PH) renewal processes as special cases, is a convenient traac model for use in the performance analysis of Asyn-chronous Transfer Mode (ATM) networks. In ATM networks, packets are of xed length and the buuering memory in switching nodes is limited to a nite number K of cells. Thes...

We consider a class of two-queue polling systems with exhaustive service, where the order in which the server visits the queues is governed by a discrete-time Markov chain. For this model, we derive an expression for the probability generating function of the joint queue length distribution at polling epochs. Based on these results, we obtain explicit expressions for the Laplace-Stieltjes trans...

We explore a queuing system with a non-homogeneous population of customers in the sense of optimizing the social welfare. In particular we modify Naor’s observable M/M/1 queue model, which is the most seminal queueing model involving strategic customers. We assume that some customers obey the central planner, who aims to maximize the social welfare, the others don’t. We consider two levels of c...

Consider a single-server queue with a Poisson arrival process and exponential processing times in which each customer independently reneges after an exponentially distributed amount of time. We establish that this system can be approximated by either a reflected Ornstein–Uhlenbeck process or a reflected affine diffusion when the arrival rate exceeds or is close to the processing rate and the re...

A tandem retrial queue consisting of two stations is studied. The first station has a single server. An input flow at the first station is described by the Markovian Arrival Process ( MAP ). If a customer from this flow meets the busy server, it goes to the orbit of infinite size and tries its luck later on in exponentially distributed random time. The service time distribution at the first sta...

We consider a state-dependent Mn/Gn/1 queueing system with both finite and infinite buffer sizes. We allow the arrival rate of customers to depend on the number of people in the system. Service times are also statedependent and service rates can be modified at both arrivals and departures of customers. We show that the steady-state solution of this system at arbitrary times can be derived using...

This paper introduces an analytical method for approximating the performability of a firm realtime system modeled by a multi-server queue. The service discipline in the queue is earliestdeadline-first (EDF), which is an optimal scheduling algorithm. Real-time jobs with exponentially distributed relative deadlines arrive according to a Poisson process. All jobs have deadlines until the end of se...

We study a statistical multiplexer that is modelled as a discrete-time single-server queueing system with infinite capacity. At the input of the multiplexer, there is a possibly unbounded population of users that generate ‘low-speed’ messages. Each such message is composed of a variable number of fixed-length packets which consecutively enter the queue at the speed of one packet per time slot. ...

existence of capacity drop phenomenon, as the difference between pre-queue and queue discharge flow rates, has been one of the controversial concepts of traffic engineering. several researches have focused on capacity drop existence and also its estimation issues. this paper aims to estimate capacity drop based not only on a comparison between breakdown and queue discharge flow rates, but also ...

Traditional product form property of Markovian queueing networks usually is vanished when capacity of queues are finite and clients are blocked or rejected. A new efficient simulation method, derived from Propp & Wilson (Propp 1996) perfect simulation, is applied to the finite capacity queues context. We present an algorithm that samples directly states of the network according to stationary di...