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Queueing Systems, 3 (1988) 277-288 277 A GENERALIZATION OF THE ERLANG FORMULA
 

Summary: Queueing Systems, 3 (1988) 277-288 277
A GENERALIZATION OF THE ERLANG FORMULA
OF TRAFFIC ENGINEERING
V. ANANTHARAM *
Department of Electrical Engineering, Phillips Hall, Cornell University, Ithaca, New York 14853,
U.S.A.
B. GOPINATH and D. HAJELA
Bell Communications Research, Inc., 435 South Street, Morristown, New Jersey 07960, U.S.A.
Received 9 September 1986
Revised 16 November 1987
Abstract
Calls arrive at a switch, where they are assigned to any one of the available idle outgoing
links. A call is blocked if all the links are busy. A call assigned to an idle link may be
immediately lost with a probability which depends on the link. For exponential holding times
and an arbitrary arrival process we show that the conditional distribution of the time to reach
the blocked state from any state, given the sequence of arrivals, is independent of the policy
used to route the calls. Thus the law of overflow traffic is independent of the assignment
policy. An explicit formula for the stationary probability that an arriving call sees the node
blocked is given for Poisson arrivals. We also give a simple asymptotic formula in this case.
Keywords: Erlang formula, blocking probability, queueing

  

Source: Anantharam, Venkat - Department of Electrical Engineering and Computer Sciences, University of California at Berkeley

 

Collections: Engineering