<p>In this article, we consider an <i>M/G/1</i> retrial queue with single server that can communicate two-way calls. The server makes outgoing calls during downtime and answers to incoming calls that come in from external sources in accordance with the Poisson process. The duration of both incoming and outgoing calls has the same arbitrary distribution. An incoming call enters an orbit when it finds the server is occupied and attempts to access the server again after a period of exponentially distributed retrial time. The entire study in this article is carried out using the theory of differential-difference equations and the supplementary variable technique. We then convert the differential-difference equations into probability generating functions. The roots approach is used to retrieve the orbit length distribution at a random epoch. The most challenging aspect of this study is to develop an analytically simple approach for determining the waiting time distribution. Additionally, we compute several valuable performance metrics, including the mean number of incoming calls in the orbit, mean waiting time in the orbit of an incoming call and the probability of the server being either idle or engaged in handling incoming and outgoing calls. Some numerical results are used to illustrate the system performance measure.</p>

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Analytical study of two-way communication in M/G/1 retrial queue with constant retrial policy

  • KM Rashmi,
  • S. K. Samanta

摘要

In this article, we consider an M/G/1 retrial queue with single server that can communicate two-way calls. The server makes outgoing calls during downtime and answers to incoming calls that come in from external sources in accordance with the Poisson process. The duration of both incoming and outgoing calls has the same arbitrary distribution. An incoming call enters an orbit when it finds the server is occupied and attempts to access the server again after a period of exponentially distributed retrial time. The entire study in this article is carried out using the theory of differential-difference equations and the supplementary variable technique. We then convert the differential-difference equations into probability generating functions. The roots approach is used to retrieve the orbit length distribution at a random epoch. The most challenging aspect of this study is to develop an analytically simple approach for determining the waiting time distribution. Additionally, we compute several valuable performance metrics, including the mean number of incoming calls in the orbit, mean waiting time in the orbit of an incoming call and the probability of the server being either idle or engaged in handling incoming and outgoing calls. Some numerical results are used to illustrate the system performance measure.