Simple Bounds and Monotnicity the Call Congestion of Finite Multiserver Delay Systems
- 1 January 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Probability in the Engineering and Informational Sciences
- Vol. 2 (1) , 129-138
- https://doi.org/10.1017/s026996480000067x
Abstract
Simple and insensitive lower and upper bounds are proposed for the call congestion of M/GI/c/n queues. To prove them we establish the general monotonicity property that increasing the waiting room and/or the number of servers in a /GI/c/n queue increases the throughput. An asymptotic result on the number of busy servers is obtained as a consequence of the bounds. Numerical evidence as well as an application to optimal design illustrates the potential usefulness for engineering purposes. The proof is based on a sample path argument.Keywords
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