Admission control for finite capacity queueing model with general retrial times and state-dependent rates

Abstract

The finite state dependent queueing model with F-policy is investigated by considering the general retrial attempts. On arrival in the system, if the job finds the server engaged, it is forced to enter into the retrial orbit. After a random period of time, the job from the retrial orbit re-attempts for the service. According to F-policy, as the system attains its full capacity, the arrivals are restricted to join the system until the number of jobs comes down to the prefixed threshold value 'F '. The supplementary variable corresponding to the remaining retrial time is used to frame the governing equations which are solved by using Laplace-Stieltjes transform and then applying the recursive method. Special models for machine repair and time-sharing queue are deduced by setting the state dependent rates. Several system indices are obtained explicitly which are further used to facilitate the sensitivity analysis by considering a numerical illustration. A cost function is constructed and minimized for evaluating the optimal threshold parameter and optimal service rate.

Fuzzy Cost Optimization for Single Server Queue under Admission Control F-policy and Balking

“…The cost function given in Equation ( 28) is a function of service rate (µ), the direct search method (Jain and Sanga (2020a)) is applied to minimize the cost function corresponding to µ.…”

“…They established the steady-state analytical formulae for various performance indices. The finite state-dependent queueing system with admission control F -policy and general retrial attempt developed by Jain and Sanga (2020a). They used the recursive method to find system performance indices and derived the cost function.…”

Packets’ Congestion Management with Fuzzy Admission Control Policy for Differentiated Service Networks

“…The management problem of queueing system with F-policy and a startup time to solve the problem of admission in a queueing system was studied by Zhang et al [14]. The researchers used the supplementary variable technique and recursive method for obtaining the steady-state probability distribution of the number of customers in the system.…”

Reliability-based measure of a retrial machine repair problem with working breakdowns under the F-policy

“…A cost model was framed to determine the optimal threshold parameter and optimal service rate. The finite state dependent queueing model with general retrial times operating under F -policy was explored by Jain and Sanga (2019c) . Sensitivity analysis of the cost function with numerical illustrations were provided.…”