Abstract
Retrial queue under consideration is the model of call center operator switching between input and outgoing calls. Incoming calls form a Poisson point process. Upon arrival, an incoming call occupies the server for an exponentially distributed service time if the server is idle. If the server if busy, an incoming call joins the orbit to make a delay before the next attempt to take the server. The probability distribution of the length of delay is an exponential distribution. Otherwise, the server makes outgoing calls in its idle time. There are multiple types of outgoing calls in the system. Outgoing call rates are different for each type of outgoing call. Durations of different types of outgoing calls follow distinct exponential distributions. Unsteadiness is that the server crashes after an exponentially distributed time and needs recovery. The rates of breakdowns and restorations are different and depend on server state. Our contribution is to obtain the probability distribution of the number of calls in the orbit under high rate of making outgoing calls limit condition. Based on the obtained asymptotics, we have built the approximations of the probability distribution of the number of calls in the orbit.
Highlights
Blended call centers are an efficient and productive implement in modern companies
1, if the server is idle, if an incoming call is in service, if an outgoing call of type n is in service, n = 2, N, if the server is in recovery state
The main contribution of this research is the solution of the system (2) by using an asymptotic analysis method under high rate of outgoing calls limit condition
Summary
Blended call centers are an efficient and productive implement in modern companies. In addition to the usual call center features they can provide both incoming and outgoing calls. In its idle time the server initiates an outgoing call. Such behaviour allows to increase the effectiveness of the system. In retrial queues the customers that find the server busy repeat their request for service after a random delay. Retrial queues are usually the models of telecommunication and random access systems and their modifications allow to describe various real systems. We consider retrial queue with two-way communication and unreliable server. Two-way communication arose as a modification of retrial queues for modeling call centers with mixed calls. To study the model we use asymptotic analysis method under high rates of making outgoing calls condition [14]
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