A converse to the output theorem of queueing theory: A martingale approach

2006 ◽  
pp. 21-28 ◽  
Author(s):  
Armand M. Makowski
Keyword(s):  
Queueing Theory ◽  
Martingale Approach

A martingale approach to the PASTA property

1993 ◽  
Vol 30 (01) ◽  
pp. 252-257
Author(s):  
Michael Scheutzow
Keyword(s):  
Poisson Process ◽  
Queueing Theory ◽  
Point Processes ◽  
Law Of Large Numbers ◽  
Boundedness Condition ◽  
Martingale Approach ◽  
Large Numbers ◽  
Poisson Arrivals ◽  
Time Averages ◽  
Image Position

It is known (Weizsäcker and Winkler (1990)) that for bounded predictable functions H and a Poisson process with jump times exists almost surely, and that in this case both limits are equal. Here we relax the boundedness condition on H. Our tool is a law of large numbers for local L 2-martingales. We show by examples that our condition is close to optimal. Furthermore we indicate a generalization to point processes on more general spaces. The above property is called PASTA (‘Poisson arrivals see time averages') and is heavily used in queueing theory.

A martingale approach to the PASTA property

1993 ◽  
Vol 30 (1) ◽  
pp. 252-257
Author(s):  
Michael Scheutzow
Keyword(s):  
Poisson Process ◽  
Queueing Theory ◽  
Point Processes ◽  
Law Of Large Numbers ◽  
Boundedness Condition ◽  
Martingale Approach ◽  
Large Numbers ◽  
Poisson Arrivals ◽  
Time Averages ◽  
Image Position

It is known (Weizsäcker and Winkler (1990)) that for bounded predictable functions H and a Poisson process with jump times exists almost surely, and that in this case both limits are equal. Here we relax the boundedness condition on H. Our tool is a law of large numbers for local L2-martingales. We show by examples that our condition is close to optimal. Furthermore we indicate a generalization to point processes on more general spaces. The above property is called PASTA (‘Poisson arrivals see time averages') and is heavily used in queueing theory.

The Approximation of Sum of Independent Distributions by the Erlang Distribution Function

2002 ◽  
Vol 7 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Antanas Karoblis
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Erlang Distribution ◽  
Estimation Of Error

The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

Book Review:Introduction to Queueing Theory. Robert B. Cooper

1973 ◽  
Vol 46 (4) ◽  
pp. 649
Author(s):  
E. G. Coffman, Jr.
Keyword(s):  
Queueing Theory
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