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# Accession Number:

## AD0652833

# Title:

## THE MATHEMATICAL THEORY OF A STATIONARY QUEUE,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Report Date:

## 1967-05-23

# Pagination or Media Count:

##
16.0

# Abstract:

## The case of a single channel is treated under the assumption that the sequence of waiting times is stationary in mean neither increasing nor decreasing and the service times have an arbitrary distribution with characteristic function psixi. The relative lengths Pk of the time intervals with k customers waiting is determined by recurrence formulas. Formula 5 gives the mean waiting time gamma mu k signifies here the k-th moment of the distribution of waiting times and alpha denotes the traffic intensity. The formula for phixi gives an expression for the characteristic function for the waiting time distribution. Finally, formula 9 gives the variance of the waiting times.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#