| The M/M/∞service System with Ranked Servers in Heavy Traffic 1984 Edition Contributor(s): Newell, G. F. (Author), Ferschl, F. (Introduction by) |
|
 |
ISBN: 3540133771 ISBN-13: 9783540133773 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback Published: September 1984 |
| Additional Information |
| BISAC Categories: - Gardening - Business & Economics | Operations Research - Business & Economics | Economics - Theory |
| Dewey: 330.1 |
| Series: Lecture Notes in Economic and Mathematical Systems |
| Physical Information: 0.31" H x 6.69" W x 9.61" (0.53 lbs) 129 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: We are concerned here with a service facility consisting of a large (- finite) number of servers in parallel. The service times for all servers are identical, but there is a preferential ordering of the servers. Each newly arriving customer enters the lowest ranked available server and remains there until his service is completed. It is assumed that customers arrive according to a Poisson process of rate A, that all servers have exponentially distributed service times with rate and that a = A/ is large compared with 1. Generally, we are concerned with the stochastic properties of the random function N(s, t) describing the number of busy servers among the first s ordered servers at time t. Most of the analysis is motivated by special applications of this model to telephone traffic. If one has a brunk line with s primary channels, but a large number (00) of secondary (overflow) channels, each newly arriving customer is assigned to one of the primary channels if any are free; otherwise, he is assigned to a secondary channel. The primary and secondary channels themselves could have a preferential ordering. For some purposes, it is convenient to imagine that they did even if an ordering is irrelevant. |