Statistics and Actuarial Science

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Browsing Statistics and Actuarial Science by Subject "Accumulating priority"

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    A Generalization of M/G/1 Priority Models via Accumulating Priority
    (University of Waterloo, 2016-01-08) Fajardo, Val Andrei
    Priority queueing systems are oftentimes set up so that arriving customers are placed into one of $N$ distinct priority classes. Moreover, to determine the order of service, each customer (upon arriving to the system) is assigned a priority level that is unique to the class to which it belongs. In static priority queues, the priority level of a class-$k$ ($k=1,2,\ldots,N$) customer is assumed to be constant with respect to time. This simple prioritization structure is easy to implement in practice, and as such, various types of static priority queues have been analyzed and subsequently applied to real-life queueing systems. However, the assumption of constant priority levels for the customers may not always be appropriate. Furthermore, static priority queues can often display poor system performance as their design does not provide systems managers the means to balance the classical trade-off inherent in all priority queues, that is: reducing wait times of higher priority customers consequently increases the wait times for those of lower priority. An alternative to static priority queues are accumulating priority queues, where the priority level of a class-$k$ customer is assumed to accumulate linearly at rate $b_k>0$ throughout the class-$k$ customer's time in the system. The main benefit of accumulating priority queues is the ability, through the specification of the accumulating priority rates $\{b_k\}_{k=1}^N$, to control the waiting times of each class. In the past, due to the complex nature of the accumulating prioritization structure, the control of waiting times in accumulating priority queues was limited --- being administered only through their first moments. Nowadays, with the advent of a very useful tool called the maximal priority process, it is possible to characterize the waiting time distributions of several types of accumulating priority queues. In this thesis, we incorporate the concept of accumulating priority to several previously analyzed static priority queues, and use the maximal priority process to establish the corresponding steady-state waiting time distributions. In addition, since static priority queues may be captured from accumulating priority queues, useful comparisons between the considered accumulating priority queues and their static priority counterparts are made throughout this thesis. Thus, in the end, this thesis results in a set of extensive analyses on these highly flexible accumulating priority queueing models that provide a better understanding of their overall behaviour, as well as exemplify their many advantages over their static priority equivalents.
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    On a general mixed priority queue with server discretion
    (Taylor & Francis, 2016-10-01) Fajardo, Val Andrei; Drekic, Steve
    We consider a single-server queueing system which attends to N priority classes that are classified into two distinct types: (i) urgent: classes which have preemptive resume priority over at least one lower priority class, and (ii) non-urgent: classes which only have non-preemptive priority among lower priority classes. While urgent customers have preemptive priority, the ultimate decision on whether to interrupt a current service is based on certain discretionary rules. An accumulating prioritization is also incorporated. The marginal waiting time distributions are obtained and numerical examples comparing the new model to other similar priority queueing systems are provided.
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    Waiting Time Distributions in the Preemptive Accumulating Priority Queue
    (Springer, 2017-03-01) Fajardo, Val Andrei; Drekic, Steve
    We consider a queueing system in which a single server attends to N priority classes of customers. Upon arrival to the system, a customer begins to accumulate priority linearly at a rate which is distinct to the class to which it belongs. Customers with greater accumulated priority levels are given preferential treatment in the sense that at every service selection instant, the customer with the greatest accumulated priority level is selected next for servicing. Furthermore, the system is preemptive so that the servicing of a customer is interrupted for customers with greater accumulated priority levels. The main objective of the paper is to characterize the waiting time distributions of each class. Numerical examples are also provided which exemplify the true benefit of incorporating an accumulating prioritization structure, namely the ability to control waiting times.