Mathematical modelof the trade as a queuing system of M/M/1/∞ type with the refusal of queuing. Part 2. Theflow of cancelled from service orders

The queuing system with Poisson flow of orders with parameter λ is analyzed. Time of servicehas exponential distribution with parameter μ. Let ribe probability that the given order arrivingat the system when i orders are waiting for a service in the line, will not stand in a queueand leaves the system. The first paper studies queuing system in which the order arriving at thesystem with a queue of length i with probability ri,0≤ ri ≤ 1 will not stand in a queue. The firstpart of this paper the characteristics of leaving order flow is investigated. The second part of thispaper contains the study of the flow of orders which denied the service. Explicit formulas for anaverage number of events in a flow are obtained. By the method of asymptotic analysis suggestedby A.A. Nazarov in conditions of increasing service time we have got asymptotic expressions formathematical expectation and variance of events in the leaving (unserved) flow.

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