Some aspects of balking and reneging in finite buffer queues

Abstract

In this paper, a single server finite buffer Markovian queuing system is analyzed with the additional restriction that customers may balk as well as renege. Reneging considered in literature is usually of position independent type where the reneging rate is constant irrespective of the position of the customer in the system. However there are many real world situations where this assumption does not hold. This paper is an attempt to model balking with position dependent reneging. Explicit closed form expressions of a number of performance measures are presented. A typical problem is discussed to demonstrate the usefulness of results derived in the paper.

Aspects of Impatience in a Finite Buffer Queue

“…An increase in system size translates to lowering of the fraction of time the server is idle. Similar conclusions can be drawn under R EOS [18].…”

“…A numerical example with design aspects was also discussed to demonstrate results derived. Choudhury and Medhi [18] also analyzed a single server finite buffer Markovian queuing model M/M/1/K with the additional restriction that customers may balk as well as renege. In this paper, balking along with position dependent reneging was considered.…”

Optimization of Balking and Reneging Queue with Vacation Interruption underN-Policy

“…The model reduces to / /1/ queue with multiple working vacations and vacation interruption. We can obtain the steady-state probabilities 0, (0 ≤ ≤ ) and 1, (1 ≤ ≤ ) from (8)- (9), where…”

“…A computational algorithm and parameter optimization for a multiserver queue with unreliable server and impatient customers have been discussed by Chia and Jau-Chaun [8]. Choudhury and Medhi [9] presented some aspects of balking and reneging in finite buffer queue. Recently, Rakesh and Sumeet [10] studied an / /1/ queueing model with retention of reneged customers and balking.…”

An SMDP model for a multiclass multi-server queueing control problem considering conversion times

“…They solve the approximating diffusion control problem (DCP) and obtain a convenient analytic expression for the infinite horizon expected average cost as a function of the threshold level. Choudhury and Pallabi [6] and Pallabi and Choudhury [15] analyze a single server Markovian queuing system and a multiserver Markovian queuing system with limited waiting space under the assumption that customers may balk as well renege.…”