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- Title
Sharp and simple bounds for the Erlang delay and loss formulae.
- Authors
Harel, Arie
- Abstract
We prove some simple and sharp lower and upper bounds for the Erlang delay and loss formulae and for the number of servers that invert the Erlang delay and loss formulae. We also suggest simple and sharp approximations for the number of servers that invert the Erlang delay and loss formulae. We illustrate the importance of these bounds by using them to establish convexity proofs. We show that the probability that the M/ M/ s queue is empty is a decreasing and convex function of the traffic intensity. We also give a very short proof to show that the Erlang delay formula is convex in the traffic intensity when the number of servers is held constant. The complete proof of this classical result has never been published. We also give a very short proof to show that the Erlang delay formula is a convex function of the (positive integer) number of servers. One of our results is then used to get a sharp bound to the Flow Assignment Problem.
- Subjects
ERLANG (Computer program language); PROGRAMMING languages; CONVEX functions; REAL variables; PROBABILITY theory
- Publication
Queueing Systems, 2010, Vol 64, Issue 2, p119
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-009-9152-7