Preemption control of multi-class loss networks

This thesis addresses the analysis and optimization of preemption in multi-class loss networks. Preemption, admission control and rate adaptation, are control mechanisms that enable loss network operators to provide quality of service (QoS) guarantees for admitted calls. This research includes two parts: i) performance characterization of a two parallel link loss network servicing multiple classes of calls under a speci c preemption and admission policy, and ii) preemption and admission control policy analysis for a single loss link servicing two classes of calls.In Part I, we consider a two parallel link multi-class loss network, where a call may preempt, if necessary, any calls with lower priorities and may in turn be preempted by any calls with higher priorities. The preemption policy permits both preemption from a preferred link to a backup link if possible, and eviction from either link if necessary. Our contributions in this part include: i) characterizing the rates of each class causing preemption of active lower priority calls, and therates of each class being preempted by an arriving higher priority call in Erlang-B functions when all classes share a common service rate; ii) simple expressions of these preemption rates through uniform asymptotic approximation; and iii) asymptotic approximation of these preemption rates using nearly completely decomposable (NCD) Markov chain techniques when classes have individual service rates.After analyzing the performance of a typical policy, we would also like to study various policies. In Part II, we analyze di erent preemption and admission control policies for a two-class loss link where per-class revenue is earned per unit time for each active call, and an instantaneous preemption cost is incurred whenever the preemption mechanism is employed. Our contributions in this part include: i) showing that under reasonable reward models, if we always preempt when the link is full, then it is better not to preempt at non-full states; ii) a su cient condition under which the average revenue of optimal preemption policy without admission control exceeds that of optimal admission control policy without preemption, which are established via policy improvement theorems fromstochastic dynamic programming.Ph.D., Computer Engineering -- Drexel University, 201

A Generalization of M/G/1 Priority Models via Accumulating Priority

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

Discrete-time queueing models with priorities

This PhD-dissertation contains analyses of several discrete-time two-class priority queueing systems. We analyze non-preemptive, preemptive resume as well as preemptive repeat priority queues. The analyses are heavily based on probability generating functions that allow us to calculate moments and tail probabilities of the system contents and packet delays of both classes. The results are applicable in heterogeneous telecommunication networks, when delay-sensitive traffic gets transmission priority over best-effort traffic. Our results predict the influence of priority scheduling on the QoS (Quality-of-Service) of the different types of traffic