On a processor sharing queue that models balking

Q. Zhen, J.S.H. Leeuwaarden, van, C. Knessl

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

2 Citaten (Scopus)


We consider the processor sharing M/M/1-PS queue which also models balking. A customer that arrives and sees n others in the system "balks" (i.e., decides not to enter) with probability 1-b n . If b n is inversely proportional to n + 1, we obtain explicit expressions for a tagged customer’s sojourn time distribution. We consider both the conditional distribution, conditioned on the number of other customers present when the tagged customer arrives, as well as the unconditional distribution. We then evaluate the results in various asymptotic limits. These include large time (tail behavior) and/or large n, lightly loaded systems where the arrival rate ¿ ¿ 0, and heavily loaded systems where ¿ ¿ 8. We find that the asymptotic structure for the problem with balking is much different from the standard M/M/1-PS queue. We also discuss a perturbation method for deriving the asymptotics, which should apply to more general balking functions.
Originele taal-2Engels
Pagina's (van-tot)453-476
TijdschriftMathematical Methods of Operations Research
Nummer van het tijdschrift3
StatusGepubliceerd - 2010


Duik in de onderzoeksthema's van 'On a processor sharing queue that models balking'. Samen vormen ze een unieke vingerafdruk.

Citeer dit