Two tandem queues with general renewal input. 2: Asymptotic expansions for the diffusion model

Journal Article · Fri Oct 01 00:00:00 EDT 1999 · SIAM Journal on Applied Mathematics (Society for Industrial and Applied Mathematics)

DOI:https://doi.org/10.1137/S0036139997328477· OSTI ID:20005556

Knessl, C; Tier, C

In Part 1 the authors formulated and solved a diffusion model for two tandem queues with exponential servers and general renewal arrivals. They thus obtained the easy traffic diffusion approximation to the steady state joint queue length distribution for this network. Here they study asymptotic and numerical properties of the diffusion approximation. In particular, analytical expressions are obtained for the tail probabilities. Both the joint distribution of the two queues and the marginal distribution of the second queue are considered. They also give numerical illustrations of how this marginal is affected by changes in the arrival and service processes.

• Research Organization: Univ. of Illinois, Chicago, IL (US)
• Sponsoring Organization: USDOE
• OSTI ID: 20005556
• Journal Information: SIAM Journal on Applied Mathematics (Society for Industrial and Applied Mathematics), Vol. 59, Issue 6; Other Information: PBD: Oct 1999; ISSN 0036-1399
• Country of Publication: United States
• Language: English

Related Subjects

99 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
QUEUES
MATHEMATICAL MODELS
INTEGRAL EQUATIONS
MATHEMATICS