This paper studies an infinite-server queue in a Markov environment, that is, an infiniteserver queue with arrival rates and service times depending on the state of a Markovian background process. Scaling the arrival rates λi by a factor N , tail probabilities are examined when letting N tend to∞; non-standard large deviations results are obtained. An importance-sampling based estimation algori...

A state-dependent 1-limited polling model with N queues is analyzed. The routing strategy generalizes the classical Markovian polling model, in the sense that two routing matrices are involved, the choice being made according to the state of the last visited queue. The stationary distribution of the position of the server is given. Ergodicity conditions are obtained by means of an associated dy...

We present an overview of recent results related to the single server queue with general independent and identically distributed service times and a batch Markovian arrival process (BMAP). The BMAP encompasses a wide range of arrival processes and yet, mathematically, the BMAP/G/I model is a relatively simple matrix generalization of the M/G/l queue. Stationary and transient distributions for t...

We consider a finite-buffer single-server queue with Markovian arrival process (MAP) where the server serves a limited number of customers, and when the limit is reached it goes on vacation. Both singleand multiple-vacation policies are analyzed and the queue length distributions at various epochs, such as pre-arrival, arbitrary, departure, have been obtained. The effect of certain model parame...

1 Abstract We consider a single-server multi-queue system with unlimited-size batch service 1 where the next queue to be served is the one with the most senior customer (the so called 2 ‘Israeli Queue’). We study a Markovian system with state-dependent group-joining policy 3 and derive results for various performance measures, such as steady-state distribution of 4 the number of groups in the s...

Abstract Here a two-state batch arrivals and batch service Markovian queue with server vacation model has been taken into consideration for its mathematical modelling and performance analysis under transient state. The present Markovian queueing model considers a single server with multiple vacations and both arrivals and services in batches of variable size. Arriving customers are processed by...

:هلاقم هصلاخ This paper introduces an analytical method for approximating the performance of a -soft real-time system consisting of a number of parallel infinite-capacity single -server queues. The service discipline for the individual queues is earliest-deadline first (EDF). Real-time jobs with exponentially distributed relative deadlines arrive according to a Poisson process. Jobs either all ...

In this paper, we present the results of a study priority multi-server queuing system with heterogeneous customers arriving according to marked Markovian arrival process (MMAP), phase-type service times (PH), and queue finite capacity. Priority traffic classes differ in PH distributions time probability joining queue, which depends on current length queue. If is full, customer does not enter sy...

Fairness is an inherent and fundamental factor of queue service disciplines in a large variety of queueing applications. Service time variability across jobs is an important factor affecting both system performance and scheduling rules (for example, computer systems that prioritize short jobs over long jobs). Service time variability and its effects on mean response times have been studied exte...

In this paper, we consider a discrete-time single-server queueing system with a generalized switched batch Bernoulli arrival and a general service time processes (a generalized SBBP=G=1 queue). Customers arrive to the system in batches and service times of customers are generally distributed. The batch size and the service time distributions are governed by a discrete-time alternating renewal p...