Abstract
A queueing system occurs when “customers” arrive at some facility requiring a certain type of “service” provided by the “servers”. Both the arrival pattern and the service requirements are usually taken to be random. If all the servers are busy when customers arrive, they usually wait in line to get served. Queues possess a number of mathematical challenges and have been mainly approached from a probability point of view, and statistical analysis are very scarce. In this paper we present a Bayesian analysis of a Markovian queue in which customers are immediately served upon arrival, and hence no waiting lines form. Emergency and self-service facilities provide many examples. Technically such services can be modelled as queues with an infinite number of servers. The mathematical simplicity of these queues allows for closed-form exploration of a number of issues that arise when statistically analyzing queues, whether or not the queue is in equilibrium.
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