A Unified Method of Analysis for Queues with Markovian Arrivals

A Unified Method of Analysis for Queues with Markovian Arrivals

We deal with finite-buffer queueing systems fed by a Markovian point process. This class includes the queues of type M/G/1/N, M/G/1/N, PH/G/1/N, MMPP/G/1/N, MAP/G/1/N, and BMAP/G/1/N and is commonly used in the performance evaluation of network traffic buffering processes. Typically, such queueing systems are studied in the stationary regime using matrixanalytic methods connected with M/G/1-typ...

Processor-sharing and Random-service Queues with Semi-markovian Arrivals

We consider single-server queues with exponentially distributed service times, in which the arrival process is governed by a semi-Markov process (SMP). Two service disciplines, processor sharing (PS) and random service (RS), are investigated. We note that the sojourn time distribution of a type-l customer who, upon his arrival, meets k customers already present in the SMP/M/1/PS queue is identi...

Analysis of Queues with Bat h Arrivals

The steady state distribution of quasi-birth-death pro esses an be eÆ iently obtained by matrix-geometri (MG) methods. Sin e a number of tele ommuni ation problems are modelled by pro esses with bat h arrivals, the extension of MG methods for these pro esses has pra ti al importan e. This paper presents an extension of MG methods whi h is e e tive for the analysis of quasi-birth-death pro esses...

Numerical analysis of queues with batch arrivals

Analysis of Queues with Markovian Service Processes∗

Markovian service process (MSP) is a model similar to the Markovian arrival process (MAP), where arrivals are replaced with service completions. The MSP can represent various queueing models such as vacation models, N -policy models and exceptional service models. We analyze MAP/MSP/1 queues and obtain a new sort of matrix-type factorization of the vector generating function for the stationary ...