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<p>This article investigates the steady-state behavior of a single-server retrial queue in which arriving units select one of two heterogeneous service types, each followed by an optional immediate re-service of the same type. Units encountering a busy server join a retrial orbit and attempt to access the server after a random delay governed by classical retrial policy. Using the supplementary variable technique, we have derived the Laplace–Stieltjes transforms of the probability generating functions for the number of units in the orbit and in the system. The stochastic decomposition property is established, and pivotal system characteristics, such as the mean and variance of the orbit size, system size, and waiting times both in orbit and in the system are obtained. To validate the analytical results and study the effect of key system parameters, numerical experiments are conducted across three service time distributions namely, exponential, 2-stage Erlang and Hyper-exponential distribution. A cost optimization is carried out employing the parabolic method to identify the optimal arrival rate that minimizes the total expected operating cost per unit time.</p>

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Performance analysis of a single server retrial queue with two heterogeneous service under re-service policy

  • 期刊论文

  • 发表日期：

    2026年7月24日

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  • Hirak Jyoti Sarma,
  • Gautam Choudhury,
  • Anjana Begum

摘要

This article investigates the steady-state behavior of a single-server retrial queue in which arriving units select one of two heterogeneous service types, each followed by an optional immediate re-service of the same type. Units encountering a busy server join a retrial orbit and attempt to access the server after a random delay governed by classical retrial policy. Using the supplementary variable technique, we have derived the Laplace–Stieltjes transforms of the probability generating functions for the number of units in the orbit and in the system. The stochastic decomposition property is established, and pivotal system characteristics, such as the mean and variance of the orbit size, system size, and waiting times both in orbit and in the system are obtained. To validate the analytical results and study the effect of key system parameters, numerical experiments are conducted across three service time distributions namely, exponential, 2-stage Erlang and Hyper-exponential distribution. A cost optimization is carried out employing the parabolic method to identify the optimal arrival rate that minimizes the total expected operating cost per unit time.