Abstract
Objective: This study discusses a two-state multiserver retrial queueing system, where the customer may leave the system due to impatience. In this paper, we deal with the time dependent probabilities when all, some or none servers are busy. Method: For this model, we solved difference differential equations recursively and obtained the time dependent probabilities when all, some or none servers are busy. Findings: Time dependent probabilities of exact number of arrivals and exact number of departures at when all, some or none servers are busy are obtained. In this paper, some kind of verification and converting two state model into single state model are discussed. Some special cases of interest are also discussed. Novelty: In communication networks, multiple servers are used to reduce traffic congestion and improve system performance. The operation mode of a call center with repeated attempts provides an initial motivation for our study. Keywords: Impatience; Multiserver; Probability; Queueing; Retrial
Highlights
Retrial queueing models serve as the quantitative technique in evaluating the operating performance of call centers
To answer the questions regarding the system operation during time period t, we developed a two – dimensional M/M/c retrial queueing model with impatient customers in which the state of the system is given by (i, j), where i describes the exact number of arrivals in the system and j describes the exact number of departures from the system until time t
Customer impatience represents the loss in revenues and customer goodwill to the service provider
Summary
Retrial queueing models serve as the quantitative technique in evaluating the operating performance of call centers. The operation of the call center can be described as follows: when a customer call arrives, it will be served immediately if a server is available. Motivated by the impact of impatience and repeated calls in the conventional systems, Cohen(6) studied a multiserver queue with retrial pool and no waiting positions. To answer the questions regarding the system operation during time period t, we developed a two – dimensional M/M/c retrial queueing model with impatient customers in which the state of the system is given by (i, j) , where i describes the exact number of arrivals in the system and j describes the exact number of departures from the system until time t. Garg and Kumar(12) obtained explicit time dependent probabilities of exact number of arrivals and departures from the orbit of a single server retrial queue with impatient customers.
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