Transient and asymptotic behavior of synchronization processes in assembly-like queues

This paper analyzes the synchronization process of an assembly-like queueing system in which two distinct types of items/customers arrive at separate buffers, according to independent Poisson processes, so as to be synchronized into pairs at a synchronization node. Once a pair is synchronized it then queues up for service from a single server on a first-in-first-out basis as pairs. It is assumed that the service times of pairs are exponentially distributed and that the system has infinite capacity. Despite their practical significance, such queueing systems have not been adequately treated in the literature due to their transience or null recurrence. We first investigate the transient and asymptotic properties of the synchronization process’ first two moments, both analytically and numerically. Motivated by the observed asymptotic behavior, we then propose an M/M/1 approximation to describe the behavior of such assembly-like queueing systems. Finally, a numerical study of the proposed approximation reveals that it performs sufficiently well for practical applications.