Retrial Queueing System MMPP/M/1 with Impatient Calls Under Heavy Load Condition

The retrial queueing system of M=M=1 type with Poisson flow of arrivals, impatient cus- tomers, collisions and unreliable service device is considered in the paper. The novelty of our contribution is the inclusion of breakdowns and repairs of the service into our previous study to make the problem more realistic and hence more complicated. Retrial time of customers in the orbit, service time, impa- tience time of customers in the orbit, server lifetime (depending on whether it is idle or busy) and server recovery time are supposed to be exponentially distributed. An asymptotic analysis method is used to find the stationary distribution of the number of customers in the orbit. The heavy load of the system and long time patience of customers in the orbit are proposed as asymptotic conditions. Theorem about the Gaussian form of the asymptotic probability distribution of the number of customers in the orbit is formulated and proved. Numerical examples are given to show the accuracy and the area of feasibility of the proposed method

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“…Let us make the substitutions σ = ε, α = qε, u = εw, H k (u) = = F k (w, ε), k = {0, 1, 2} in basic system (11), where ε → 0.…”

Section: Stage 1 Finding the First-order Asymptoticmentioning

confidence: 99%

“…Impatience of calls in the orbit is understood as the case when a customer in the orbit can leave the orbit after a random time without service [4,5,7,[9][10][11]. But there is another way to specify impatience, for example, non-persistence, balking and reneging are used [8,[12][13][14][15].…”

mentioning

confidence: 99%