Performance Analysis of Priority Queueing Systems in Discrete Time

Priority scheduling for packets is a hot topic, as interactive (voice, video) services are being integrated in existing data networks. In this paper, we consider a discrete-time queueing system with a non-preemptive (or Head-Of-the-Line) priority scheduling discipline and a general number of priority classes. Packets of variable length arrive in the queueing system. We derive expressions for the probability generating functions of the packet delays. From these functions, some performance measures (such as moments and approximate probabilities) are calculated. We illustrate the performance measures by means of some numerical examples and show how to apply the theoretical results to a queue that handles arriving multimedia traffic.

System delay versus system content for discrete-time queueing systems subject to server interruptions

In this paper, the waiting time and response time processes in continuous-time two parallel queueing systems are analyzed as well as the system size process in discrete-time two parallel queueing systems. Upon arrival, each job splits into two tasks, denoted by task 1 and task 2. Task k, $k = 1,2$, is assigned to the kth queueing system to be served on a FCFS (first-come-first-served) basis. Each queueing system consists of a single server and an infinite-capacity queue. For the continuous-time queueing system, we assume that jobs arrive in a state-independent Poisson fashion with rate $\lambda $; the servers have exponential service times with rates $\mu _1 $ and $\mu _2 $, respectively. A closed-form expression for the Laplace transform of the ergodic bivariate waiting time distribution is derived. The distribution of the sum of the two waiting times is then obtained. The distribution of the response time when $\mu _1 = \mu _2 $ is derived analytically. For the discrete-time queueing systems, it is assu...

In high speed networks, the strict priority (SP) scheduling discipline is perhaps the most common and simplest method to schedule packets from different classes of applications, each with diverse performance requirements. With this discipline, however, packets at higher priority levels can starve packets at lower priority levels. To resolve this starvation problem, we propose to assign a parameter to each priority queue in the SP discipline. The assigned parameter determines the probability with which its corresponding queue is served when the queue is polled by the server. We thus form a new packet scheduling discipline, referred to as the probabilistic priority (PP) discipline. By properly setting the assigned parameters, service differentiation as well as fairness among traffic classes can be achieved in PP. In addition, the PP discipline can be easily reduced to the ordinary SP discipline or to the reverse SP discipline.

We analyze queueing model with priority scheduling by supplementary variable method. Customers are classified into two types (type-1 and type-2 ) according to their characteristics. Customers of each type arrive by independent Poisson processes, and all customers regardless of type have same general service time. The service order of each type is determined by the queue length of type-1 buffer. If the queue length of type-1 customer exceeds a threshold L, the service priority is given to the type-1 customer. Otherwise, the service priority is given to type-2 customer. Method of supplementary variable by remaining service time gives us information for queue length of two buffers. That is, we derive the differential difference equations for our queueing system. We obtain joint probability generating function for two queue lengths and the remaining service time. Also, the mean queue length of each buffer is derived.

The proportional delay differentiation model provides a consistent packet delay differentiation between various classes of service. The waiting time priority (WTP) scheduler is a priority scheduler in which the priority of a packet increases in proportion to its waiting time, and it is known as the best scheduler to achieve proportional delay differentiation model. This paper proposes an advance WTP (AWTP) scheduler, modified from WTP, which accounts for the packet transmission time. Simulation results reveal that when the link utilization is moderate (60%-90%), this scheduler not only obtains more accurate delay proportion than the WTP scheduler, but also reduces the average queuing delay (waiting time). The effects of traffic load distribution are also examined. However, AWTP may not maintain stable delay ratios under various traffic load distributions. A modification named AWTP/sup +/ is proposed and proven to relieve this problem.

The proportional delay differentiation model provides consistent packet delay differentiation between classes of service. The waiting time priority (WTP) scheduler is a priority scheduler in which the priority of a packet increases in proportion to its waiting time, and it is known as the best scheduler to achieve the proportional delay differentiation model. This paper proposes an advanced WTP (AWTP) scheduler, modified from WTP, that takes the packet transmission time into account. Simulation results reveal that when the link utilization is moderate (60%-90%), this scheduler not only obtains more accurate delay proportion than the WTP scheduler, but also reduces the average waiting time.

Performance evaluation of CAI and RAI transmission modes in a GI-G-1 queue

A generalized SBBP/G/1 queue and its applications

This paper proposes a unified matrix-analytic approach to characterize the output processes of general discrete-time lossless/lossy queueing systems in which time is synchronized/slotted into fixed length intervals called slots. The arrival process can be continuous- or discrete-time Markovian processes. It can be either renewal or non-renewal. The service of a customer commences at the beginning of a slot, consumes a random number of slots, and completes at the end of a later slot. The service times are independent and follow a common and general distribution. Systems with and without server vacations are both treated in this paper. These queueing systems have potential applications in asynchronous transfer mode (ATM) networks, packet radio networks, etc. Since the output process of a node in a queueing network becomes an input process to some node at the next stage, the results of this paper can be used to facilitate end-to-end performance analysis which has attracted more and more attention in the literature.

Discrete-time Geo [ X] / GH/1 retrial queue with Bernoulli feedback

Achieving differentiated services through multi-class probabilistic priority scheduling

This paper discusses a discrete-time queueing system in which an arriving customer may adopt four different strategies; two of them correspond to a LCFS discipline where displacements or expulsions occur, and in the other two, the arriving customer decides to follow a FCFS discipline or to become a negative customer eliminating the customer in the server, if any. The different choices of the involved parameters make this model to enjoy a great versatility, having several special cases of interest. We carry out a thorough analysis of the system, and using a generating function approach, we derive analytical results for the stationary distributions obtaining performance measures for the number of customers in the queue and in the system. Also, recursive formulae for calculating the steady-state distributions of the queue and system size has been developed. Making use of the busy period of an auxiliary system, the sojourn times of a customer in the queue and in the system have also been obtained. Finally, some numerical examples are given.

Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks; for instance, to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discrete-time models come natural. We start this paper with a review of suitable discrete-time queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter, etc.). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival process as well as non-FCFS scheduling are taken into account. Focus is on delay performance measures, such as the mean delay experienced by both types of packets and probability tails of these delays.

A well-known problem with priority policies is starvation of delay-tolerant traffic. Furthermore insufficient control over delay differentiation (which is needed for modern network applications) has incited the development of other scheduling disciplines. Processor sharing is one of many solutions to this problem. The priority policy we present here has the added benefit of being more open to rigorous analysis. We study a discrete-time queueing system with a single server and single queue, in which N types of customers enter (we will refer to packets as customers) pertaining to different priorities. A general i.i.d. arrival process is assumed and service times are deterministic. We divide the time axis into 'frames' of fixed size (counted as a number of time-slots), and reorder the customers that enter the system during the same frame such that the high-priority customers are served first. This paper gives an analytic approach to studying such a system, and in particular focuses on the queue content (meaning the customers of each type in the system at random slotmarks) in stationary regime. Clearly the frame's size is the key factor in the delay differentiation between the two priority classes. The numerical results at the end of this paper illustrate this fact.