Petri net analysis of a queueing inventory system with orbital search by the server

In this article, a queueing inventory system with finite sources of demands, retrial demands, service time, lead time, (s,S)\left(s,S) replenishment policy, and demands search from the orbit was studied. When the lead time is exponentially distributed (resp. lead time is generally distributed), generalized stochastic Petri net (GSPN) (resp. Markov regenerative stochastic Petri net [MRSPN]) is proposed for this inventory system. The quantitative analysis of this stochastic Petri net model was obtained by continuous time Markov chain for the GSPN model (resp. the supplementary variable method for the MRSPN model). The probability distributions are obtained, witch allowed us to compute performance measures and the expected cost rate of the studied system

Performance Analysis of the M/G/c/c+r Queuing System for Cloud Computing Data Centers

International audienceIn this paper, we propose M/G/c/c+r queuing system as a model for performance evaluation of cloud server farms. Analytical resolution of this queuing system remains, to this day, an open and challenging issue because an exact analytical solution is difficult to reach. Therefore, we provide new approximate formulas to compute the transition-probability matrix of this system. In order to examine the accuracy of our approximate formulas, we test them numerically on some examples. Then, we compute the steady-state probabilities and some performance indicators such as blocking probability, mean response time, probability of immediate service and delay probability