<p>This paper studies a single-server priority retrial queue with two classes of incoming calls and one class of outgoing calls. Arrivals follow independent Poisson processes, and class-1 incoming calls have preemptive priority over the other two classes. High-priority calls that find the server busy join a finite buffer, while blocked or preempted low-priority incoming calls enter an orbit; preempted outgoing calls leave the system. A preemptive-resume priority discipline is assumed for orbital calls, and service times are class-dependent with general i.i.d. distributions. Using a regenerative process framework, stability conditions and key performance measures are derived. For the Markovian version of the model, matrix-analytic methods provide explicit performance results, which are shown to be consistent with the regenerative analysis. An important finding is the insensitivity of system performance to the service-time distribution of low-priority incoming calls. Simulations are performed to validate the theoretical results obtained. Numerical results illustrate the effect of buffer capacity under different service distributions, and a cost function is formulated to determine the optimal buffer size in the Markovian case. The effect of service time distributions on the system performance is also studied numerically. The proposed model is motivated by communication scenarios in vehicular ad hoc networks (VANETs), where heterogeneous traffic with different priority levels competes for limited processing resources. However, this study emphasizes probabilistic modeling and analytical methodologies rather than application-specific protocol design. Thus the developed framework and results are applicable to a wide range of stochastic service systems exhibiting prioritized and retrial behavior.</p>

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Performance analysis of a single server priority retrial queue with two-way communication

  • Aswani Thomas,
  • T.G. Deepak

摘要

This paper studies a single-server priority retrial queue with two classes of incoming calls and one class of outgoing calls. Arrivals follow independent Poisson processes, and class-1 incoming calls have preemptive priority over the other two classes. High-priority calls that find the server busy join a finite buffer, while blocked or preempted low-priority incoming calls enter an orbit; preempted outgoing calls leave the system. A preemptive-resume priority discipline is assumed for orbital calls, and service times are class-dependent with general i.i.d. distributions. Using a regenerative process framework, stability conditions and key performance measures are derived. For the Markovian version of the model, matrix-analytic methods provide explicit performance results, which are shown to be consistent with the regenerative analysis. An important finding is the insensitivity of system performance to the service-time distribution of low-priority incoming calls. Simulations are performed to validate the theoretical results obtained. Numerical results illustrate the effect of buffer capacity under different service distributions, and a cost function is formulated to determine the optimal buffer size in the Markovian case. The effect of service time distributions on the system performance is also studied numerically. The proposed model is motivated by communication scenarios in vehicular ad hoc networks (VANETs), where heterogeneous traffic with different priority levels competes for limited processing resources. However, this study emphasizes probabilistic modeling and analytical methodologies rather than application-specific protocol design. Thus the developed framework and results are applicable to a wide range of stochastic service systems exhibiting prioritized and retrial behavior.