Averaging Met hods for Transient Regimes in Overloading Retrial Queueing Systems
نویسنده
چکیده
A new approach is suggested to study transient and stable regimes in overloading retrial queueing systems. This approach is based on limit theorems of averaging principle and diffusion approximation types for so-called switching processes. Two models of retrial queueing systems of the types h?/G/i/w.r (multidimensional Poisson input flow, one server with general service times, retrial system) and M/M/m/w.r (m servers with exponential service) are considered in the case when the intensity of calls that reapply for the service tends to zero. For the number of re-applying calls, functional limit theorems of averaging principle and diffusion approximation types are proved. @ 1999 Elsevier Science Ltd. All rights reserved. KeywordsRetrial queueing systems, Averaging principle, Diffusion approximation, Switching processes, Markov processes.
منابع مشابه
Sufficient stability conditions for multi-class constant retrial rate systems
We study multi-class retrial queueing systems with Poisson inputs, general service times, and an arbitrary numbers of servers and waiting places. A class-i blocked customer joins orbit i and waits in the orbit for retrial. Orbit i works like a single-server ·/M/1 queueing system with exponential retrial time regardless of the orbit size. Such retrial systems are referred to as retrial systems w...
متن کاملAnalysis of a Batch Arrival Single Service Retrial Queueing System with Threshold Policy for Modified Vacations
Five different classical bulk queueing models with variations are considered from chapter II to chapter VI. This chapter and chapter VIII are devoted for the analysis of two different retrial queueing models. Retrial queueing system is characterized by the feature that the arriving customers, who encounter the server busy, join a virtual pool called orbit. An arbitrary customer in the orbit gen...
متن کاملReliability Analysis of the Retrial Queue with Server Breakdowns and Repairs
Retrial queues have been widely used to model many problems arising in telephone switching systems, telecommunication networks, computer networks and computer systems, etc. It is of basic importance to study reliability of retrial queues with server breakdowns and repairs because of limited ability of repairs and heavy influence of the breakdowns on the performance measure of the system. Howeve...
متن کاملStandard and Retrial Queueing Systems: a Comparative Analysis
We describe main models and results of a new branch of the queueing theory, theory of retrial queues, which is characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.) leaves the service area, but after some random delay returns to the system again. Emphasis is done on comparison with standard queues wit...
متن کاملErgodicity of the BMAP/PH}/s/s+K retrial queue with PH-retrial times
Abstract Define the traffic intensity as the ratio of the arrival rate to the service rate. This paper shows that the BMAP/PH/s/s+K retrial queue with PH-retrial times is ergodic if and only if its traffic intensity is less than one. The result implies that the BMAP/PH/s/s+K retrial queue with PH-retrial times and the corresponding BMAP/PH/s queue have the same condition for ergodicity, a fact ...
متن کامل