This paper derives the strong approximation for a multiclass
queueing network,where jobs after service completion can only move to a
downstream service station. Job classes are partitioned into groups. Within a
group, jobs are served in the order of arrival; that is, a first-in first-out
(FIFO) discipline is in force, and among groups, jobs are served under a
preassigned preemptive priority discipline. We obtain the strong approximation
for the network through an inductive application of an input–output
analysis for a single-station queue. Specifically, we show that if the input
data (i.e., the arrival and the service processes) satisfy an approximation
(such as the functional law-of-iterated logarithm approximation or the strong
approximation), then the output data (i.e., the departure processes) and the
performance measures (such as the queue length, the workload and the sojourn
time processes) satisfy a similar approximation. Based on the strong
approximation, some procedures are proposed to approximate the stationary
distribution of various performance measures of the queueing network. Our work
extends and complements the existing work of Peterson and Harrison and Williams
on the feedforward queueing network. The numeric examples show that strong
approximation provides a better approximation than that suggested by a
straightforward interpretation of the heavy traffic limit theorem.