Loss and Delay System Queueing Analyses State Dependent Service Rate Birth and Death Process Peaked and Smooth Traffic
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Journal of Computing, Vol. 2, No 1, (2008), 57p-72p
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.
This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.