The impact of priority generations in a multi-priority queueing system: a simulation approach

In this paper, we consider a preemptive (multiple) priority queueing model in which arrivals occur according to a Markovian arrival process (MAP). An arriving customer belongs to priority type i, 1 ≤ i ≤ m+1, with probability p_i. The highest priority, labeled as 0, is generated by other priority customers while waiting in the system and not otherwise. Also, a customer of priority i can turn into a priority j, j ≠ i, 1 ≤ i, j ≤ m + 1, customer, after a random amount of time that is assumed to be exponentially distributed with parameter depending on the priority type. The waiting spaces for all but priority type m + 1 are assumed to be finite. The (m + 1) - st priority customers have unlimited waiting space. At any given time, the system can have at most one highest priority customer. Thus, all priority customers except the (m + 1) − st are subject to loss. Customers are served on a first-come-first-served basis within their priority by a single server and the service times are assumed to follow a phase type distribution that may depend on the customer priority type. This queueing model, which is a level-dependent quasi-birth-and-death process, is amenable for investigation algorithmically through the well-known matrix-analytic methodology. However, here we propose to study through simulation using ARENA, a powerful simulation software as some key measures such as the waiting time distributions are highly complex to characterize analytically. The simulated results for a few scenarios are presented.