Abstract:
The relationship between the waiting time, service time,
and interarrival time distributions for the G/G/l queue at
steady state is given by Lindley's integral equation. This
thesis examines Lindley's equation and provides a solution
for the waiting time distribution using Laplace transforms
and a Wiener-Hopf factorization technique. The use of the
solution method is exhibited for both continuous and discrete
cases of the random variables involved in the queueing process.
In the entirely discrete case, an improved analogue of the
solution technique is developed.
Further analysis of Lindley's equation shows that the
service time distribution may be uniquely determined (when
the waiting time and interarrival time distributions are
known); but the problem of determining an unknown inter
arrival distribution has no unique solution.
Approximation methods for solving the waiting time
distribution of the n-server queue (G/G/n) are discussed,
and an approximate solution is developed, based on the single
server solution of Lindley's equation. This approximate
solution is exact for the M/M/n system. Its accuracy for
some other service and arrival processes is illustrated by
comparing the approximated distributions with those obtained
by computer simulation using Monte Carlo techniques.
