Analysis of single server finite buffer queue under discouraged arrival and retention of reneging

Abstract

Queuing models where arrival rates go down consequent to increase in the number of customers are called systems with discouraged arrivals. Discouraged arrivals are distinct from balking in the sense that balking implies that arriving customers do not join. In this paper, we model a single server finite buffer Markovian queuing model with discouraged arrival, balking, reneging and retention of reneged customers. The steady state probabilities are obtained using Markov process method. Closed form expression of traditional as well as some freshly designed performance measures are presented. We also perform sensitivity analysis to examine the variations in performance measures with the variations in system parameters. Our results are numerically illustrated through a field level problem with design connotations.

Optimizing Resource Allocation in M/M/1/N Queues with Feedback, Discouraged Arrivals, and Reneging for Enhanced Service Delivery

“…Regardless of the number of jobs in the system, the time taken to process each job is exponentially distributed with a constant service rate. Kumar [8], Medhi & Choudhury [9], Reynolds [10] and Kumar [11] have also investigated the discouraged arrivals queue, and Sharma [12] investigated the solution of a queueing model using a triangular matrix approach. Recently, Kumar [13] discovered a solution for the singleserver multiple-vacation queue with discouragement by employing confluent hypergeometric functions.…”