Work

On an Equivalence Between Loss Rates and Cycle Maxima in Queues and Dams

Year: 2005

Type: article

Abstract: We consider the loss probability of a customer in a single-server queue with finite buffer and partial rejection and show that it can be identified with the tail distribution of the cycle maximum of the associated infinite-buffer queue. This equivalence is shown to hold for the GI/G/1 queue and for dams with state-dependent release rates. To prove this equivalence, we use a duality for stochastically monotone recursions, developed by Asmussen and Sigman (1996). As an application, we obtain several exact and asymptotic results for the loss probability and extend Takács' formula for the cycle maximum in the M/G/1 queue to dams with variable release rate.

Source: Probability in the Engineering and Informational Sciences

DOI: 10.1017/s0269964805050138

Authors: René Bekker, Bert Zwart

Institutions: Centrum Wiskunde & Informatica, Eindhoven University of Technology

Language: English

Topic: Advanced Queuing Theory Analysis

Subfield: Management Information Systems

Field: Business, Management and Accounting

Domain: Social Sciences

Open Access status: green

OpenAlex ID: W2097927709

FWCI: 2.616

Cites: 27

Cited by: 18

Related to: 10