The Heavy Traffic Approximation for Single Server Queues in Series,
Abstract
A tandem queue with K single server stations and unlimited interstage storage is considered. Customers arrive at the first station in a renewal process, and the service times at the various stations are mutually independent i.i.d. sequences. The central result shows that the equilibrium waiting time vector if distributed approximately as a random vector Z under heavy traffic conditions (meaning that the system traffic intensity is near its critical value). The weak limit Z is defined as a certain functional of multi-dimensional Brownian Motion. Its distribution depends on the underlying interarrival and service time distributions only through their first two moments. The outstanding unsolved problem is to determine explicitly the distribution of Z for general values of the relevant parameters. A general computational approach is demonstrated and used to solve for one special case. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 10, 1971
- Accession Number
- AD0728998
Entities
People
- J. Michael Harrison
Organizations
- Stanford University