An approximation model for sojourn time distributions in acyclic multi-server queueing networks

• We model the steady-state distribution of sojourn time of customers in an acyclic, multi-stage, multi-server queueing network.
• We use phase-type distributions to approximate waiting times and general processing times.
• The model can be used to predict the probability that time in a system will exceed a specified time.
• The model is especially effective for small- and medium-sized systems.

We develop an approximation model for the sojourn time distribution of customers or jobs arriving to an acyclic multi-server queueing network. The model accepts general interarrival times and general service times, and is based on the characteristics of phase-type distributions. The model produces excellent results for multi-server networks with a small to medium number of workstations, but is less accurate when the number of workstations is large.