Analysis of a multi-server queueing model with vacations and optional secondary services

Srinivas R. Chakravarthy. "Analysis of a multi-server queueing model with vacations and optional secondary services." Mathematica Applicanda 41.2 (2013): null. <http://eudml.org/doc/292906>.

@article{SrinivasR2013,
abstract = {In this paper we study a multi-server queueing model in which the customer arrive according to a Markovian arrival process. The customers may require, with a certain probability, an optional secondary service upon completion of a primary service. The secondary services are offered (in batches of varying size) when any of the following conditions holds good: (a) upon completion of a service a free server finds no primary customer waiting in the queue and there is at least one secondary customer (including possibly the primary customer becoming a secondary customer) waiting for service; (b) upon completion of a primary service, the customer requires a secondary service and at that time the number of customers needing a secondary service hits a pre-determined threshold value; (c) a server returning from a vacation finds no primary customer but at least one secondary customer waiting. The servers take vacation when there are no customers (either primary or secondary) waiting to receive service. The model is studied as a QBD-process using matrix-analytic methods and some illustrative examples arediscussed.},
author = {Srinivas R. Chakravarthy},
journal = {Mathematica Applicanda},
keywords = {Markovian arrival process, queueing, waiting time, vacation, secondary batch services, multi-service, phase type distribution, and algorithmic probability.},
language = {eng},
number = {2},
pages = {null},
title = {Analysis of a multi-server queueing model with vacations and optional secondary services},
url = {http://eudml.org/doc/292906},
volume = {41},
year = {2013},
}

TY - JOUR
AU - Srinivas R. Chakravarthy
TI - Analysis of a multi-server queueing model with vacations and optional secondary services
JO - Mathematica Applicanda
PY - 2013
VL - 41
IS - 2
SP - null
AB - In this paper we study a multi-server queueing model in which the customer arrive according to a Markovian arrival process. The customers may require, with a certain probability, an optional secondary service upon completion of a primary service. The secondary services are offered (in batches of varying size) when any of the following conditions holds good: (a) upon completion of a service a free server finds no primary customer waiting in the queue and there is at least one secondary customer (including possibly the primary customer becoming a secondary customer) waiting for service; (b) upon completion of a primary service, the customer requires a secondary service and at that time the number of customers needing a secondary service hits a pre-determined threshold value; (c) a server returning from a vacation finds no primary customer but at least one secondary customer waiting. The servers take vacation when there are no customers (either primary or secondary) waiting to receive service. The model is studied as a QBD-process using matrix-analytic methods and some illustrative examples arediscussed.
LA - eng
KW - Markovian arrival process, queueing, waiting time, vacation, secondary batch services, multi-service, phase type distribution, and algorithmic probability.
UR - http://eudml.org/doc/292906
ER -