Study of Queuing Systems with a Generalized Departure Process

Mirtchev, Seferin, and Statev, Stanimir. "Study of Queuing Systems with a Generalized Departure Process." Serdica Journal of Computing 2.1 (2008): 57-72. <http://eudml.org/doc/11453>.

@article{Mirtchev2008,
abstract = {This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.This paper deals with a full accessibility loss system and a single server delay system with a Poisson arrival process and state dependent exponentially distributed service time. We use the generalized service flow with nonlinear state dependence mean service time. The idea is based on the analytical continuation of the Binomial distribution and the classic M/M/n/0 and M/M/1/k system. We apply techniques based on birth and death processes and state-dependent service rates. We consider the system M/M(g)/n/0 and M/M(g)/1/k (in Kendal notation) with a generalized departure process Mg. The output intensity depends nonlinearly on the system state with a defined parameter: “peaked factor p”. We obtain the state probabilities of the system using the general solution of the birth and death processes. The influence of the peaked factor on the state probability distribution, the congestion probability and the mean system time are studied. It is shown that the state-dependent service rates changes significantly the characteristics of the queueing systems. The advantages of simplicity and uniformity in representing both peaked and smooth behaviour make this queue attractive in network analysis and synthesis.},
author = {Mirtchev, Seferin, Statev, Stanimir},
journal = {Serdica Journal of Computing},
keywords = {Loss and Delay System; Queueing Analyses; State Dependent Service Rate; Birth and Death Process; Peaked and Smooth Traffic; loss and delay system; queueing analyses; state dependent service rate; birth and death process; peaked and smooth traffic},
language = {eng},
number = {1},
pages = {57-72},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Study of Queuing Systems with a Generalized Departure Process},
url = {http://eudml.org/doc/11453},
volume = {2},
year = {2008},
}

TY - JOUR
AU - Mirtchev, Seferin
AU - Statev, Stanimir
TI - Study of Queuing Systems with a Generalized Departure Process
JO - Serdica Journal of Computing
PY - 2008
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 2
IS - 1
SP - 57
EP - 72
AB - This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.This paper deals with a full accessibility loss system and a single server delay system with a Poisson arrival process and state dependent exponentially distributed service time. We use the generalized service flow with nonlinear state dependence mean service time. The idea is based on the analytical continuation of the Binomial distribution and the classic M/M/n/0 and M/M/1/k system. We apply techniques based on birth and death processes and state-dependent service rates. We consider the system M/M(g)/n/0 and M/M(g)/1/k (in Kendal notation) with a generalized departure process Mg. The output intensity depends nonlinearly on the system state with a defined parameter: “peaked factor p”. We obtain the state probabilities of the system using the general solution of the birth and death processes. The influence of the peaked factor on the state probability distribution, the congestion probability and the mean system time are studied. It is shown that the state-dependent service rates changes significantly the characteristics of the queueing systems. The advantages of simplicity and uniformity in representing both peaked and smooth behaviour make this queue attractive in network analysis and synthesis.
LA - eng
KW - Loss and Delay System; Queueing Analyses; State Dependent Service Rate; Birth and Death Process; Peaked and Smooth Traffic; loss and delay system; queueing analyses; state dependent service rate; birth and death process; peaked and smooth traffic
UR - http://eudml.org/doc/11453
ER -