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Department of Statistical and Actuarial Sciences
Center of Actuarial Excellence (CAE)
Convocation June 2014
Convocation June 2014

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  • PhD Thesis Proposal Defence - Na Li (Thursday, January 08, 2015)
    Time: 3:30pm-4:00pm and Room: WSC 248
    Speaker: Na Li
    Title: The Heterogeneous Multi-Server Accumulating Priority Queue

    Historically, lengthy waiting time problems have been analyzed using classical priority queuing theory. Classical priority queues serve classes of customers according to their pre-assigned priority, meaning that no customer from a given class can be admitted into service when there are customers from classes with higher priority present in the queue. Kleinrock (1964) proposed a queue called time-dependent priority queue", where customer's pre-assigned priority changes dynamically based on how long they have waited. He suggested that customers accumulate priority according to a linear function of their waiting time in the queue, and the rate at which the customer accumulates priority depends on the customer's class. Since the performance of many queues is specified in terms of tails of waiting time distributions and not only the mean waiting times, Stanford et al. (2014) derived the waiting time distributions of different priority classes in a single server accumulating priority queue (APQ) subject to Poisson arrivals. However, in practice, often there is more than one server to handle the arriving customers in the waiting lines. Sharif et al. (2014) obtained the waiting time distributions of different priority classes for a multi-server APQ where the service time distributions are assumed to be exponentially distributed with a common parameter for all classes. Currently, we are developing a more general multi-server model whose service times are exponentially distributed with heterogeneous service rates among different servers. Numerical investigations through simulation are carried out to validate our model.

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