Two tandem queues with general renewal input -- 1: Diffusion approximation and integral representations

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/S0003613999732846· OSTI ID:20005555

Knessl, C; Tier, C

The authors consider two tandem queues with exponential servers. Arrivals to the first queue are governed by a general renewal process. If the arrivals were also exponentially distributed, this would be a simple example of a Jackson network. However, the structure of the model is much more complicated for general arrivals. They analyze the joint steady-state queue length distribution for this network, in the heavy traffic limit, where the arrival rate is only slightly less than the service rates. The formulate and solve the boundary value problem for the diffusion approximation to this model. They obtain simple integral representations for the (asymptotic) steady-state queue length distribution.

• Research Organization: Univ. of Illinois, Chicago, IL (US)
• Sponsoring Organization: USDOE
• OSTI ID: 20005555
• 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
MATHEMATICAL MODELS
BOUNDARY-VALUE PROBLEMS
QUEUES
USES
INTEGRAL EQUATIONS