Effect of class clustering on delay differentiation in priority scheduling

Priority scheduling is the most viable way to implement QoS differentiation in telecommunication networks. Most studies on priority scheduling do not take into account possible class clustering. In particular, they assume that different classes occur randomly and independently in the arrival stream of packets. In reality, however, packets of the same class may have the tendency to arrive in clusters. By using existing results, it is shown that class clustering may have a severe impact on the achievable delay differentiation in priority scheduling

Partially shared buffers with full or mixed priority

This paper studies a finite-sized discrete-time two-class priority queue. Packets of both classes arrive according to a two-class discrete batch Markovian arrival process (2-DBMAP), taking into account the correlated nature of arrivals in heterogeneous telecommunication networks. The model incorporates time and space priority to provide different types of service to each class. One of both classes receives absolute time priority in order to minimize its delay. Space priority is implemented by the partial buffer sharing acceptance policy and can be provided to the class receiving time priority or to the other class. This choice gives rise to two different queueing models and this paper analyses both these models in a unified manner. Furthermore, the buffer finiteness and the use of space priority raise some issues on the order of arrivals in a slot. This paper does not assume that all arrivals from one class enter the queue before those of the other class. Instead, a string representation for sequences of arriving packets and a probability measure on the set of such strings are introduced. This naturally gives rise to the notion of intra-slot space priority. Performance of these queueing systems is then determined using matrix-analytic techniques. The numerical examples explore the range of service differentiation covered by both models

On generalized processor sharing and objective functions: analytical framework

Today, telecommunication networks host a wide range of heterogeneous services. Some demand strict delay minima, while others only need a best-effort kind of service. To achieve service differentiation, network traffic is partitioned in several classes which is then transmitted according to a flexible and fair scheduling mechanism. Telecommunication networks can, for instance, use an implementation of Generalized Processor Sharing (GPS) in its internal nodes to supply an adequate Quality of Service to each class. GPS is flexible and fair, but also notoriously hard to study analytically. As a result, one has to resort to simulation or approximation techniques to optimize GPS for some given objective function. In this paper, we set up an analytical framework for two-class discrete-time probabilistic GPS which allows to optimize the scheduling for a generic objective function in terms of the mean unfinished work of both classes without the need for exact results or estimations/approximations for these performance characteristics. This framework is based on results of strict priority scheduling, which can be regarded as a special case of GPS, and some specific unfinished-work properties in two-class GPS. We also apply our framework on a popular type of objective functions, i.e., convex combinations of functions of the mean unfinished work. Lastly, we incorporate the framework in an algorithm to yield a faster and less computation-intensive result for the optimum of an objective function

Delay Analysis of a Discrete-Time Non-Preemptive Priority Queue with Priority Jumps

In this paper, we consider a discrete-time non-preemptive priority queueing model with priority jumps. Two classes, real-time (high priority) and non-real time (low priority), of traffic will be considered with providing jumps from lower priority traffic to the queue of high priority traffic. We derive expressions for the joint probability generating function of the system contents of the high and the low priority traffic in the steady state and also for some performance measures such as the mean value of the system contents and the packet delay. The behavior of the priority queues with priority jumps will be illustrated by using these results and is compared to the FIFO scheme

Uncovering the evolution from finite to infinite high-priority capacity in a priority queue

Infinite capacity queues are often used as approximation for their finite real-world counterparts as they are mathematically tractable. It is generally known that tail probabilities of low-priority system content in a two-class priority queue with infinite capacity for customers of both priority classes can be non-exponential, even if the interarrival time and service time distributions are exponentially decaying. In contrast, when the capacity for the high-priority customers is finite, tail probabilities of low-priority system content are always exponentially decaying. Therefore, using the results for one as an (accurate) approximation for the other is not obvious. From an analytical point of view, the non-exponentiality in the infinite case is caused by the arisal of an implicitly defined function, a root of the kernel, in the probability generating function for the low-priority system content. However, up till now, it has been unclear how this non-exponentiality suddenly emerges when taking the limit from to the finite to the infinite case. Our main contribution is that, under the restriction of a maximum of two arrivals per slot, a recurrence relation in the high-priority capacity is constructed resulting in an explicit expression for the corresponding generating function for the finite case. Amazingly, this expression contains all roots of the kernel in the infinite case. Taking the limit of this expression leads to the well-known behavior for the infinite case as the root inside the complex unit circle dominates the other roots uncovering the evolution from the finite to the infinite case. Furthermore, we investigate under which circumstances the standard tail characterizations are inaccurate