On the analysis of priority scheduling and its applications in the M/G/1 queueing system (original) (raw)
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International Journal of Science and Society, 2011
In this work, single-server queues were studied where the inter-arrival time and service time were Markovian. This was with a view to deriving formulae for the mean number of customers, mean service time as well as mean sojourn time in the system and on the queue. A single server queue with Markov inter-arrivals and service time was considered through its time-dependent behavior, transition diagram, limiting behavior, and recursion process to arrive at the probability of having an nth customer in the system. The mean performance measure was considered to arrive at the mean for service time, waiting time, and sojourn time for the customer in the queue and in the system. The mean parameters for some priority cases such as pre-emptive resume priority and non-preemptive priority were then derived and applied in determining the generating function P(Z) of the customers in the system, the distribution of the number of customers in the system, the mean number of customer in the system, the distribution of the number of customers in the system, the Laplace-Stieltjes transform of the sojourn time, the mean and the distribution of sojourn time, the mean busy period duration. The study concluded that the above models generalized the Markov Inter-arrival and service time queue model for priority cases.
Analyzing multi-class, multi-server queueing systems with preemtive priorities
2002
In this paper we consider a multi-class, multi-server queueing system with preemptive priorities. We distinguish two groups of priority classes that consist of multiple items, each having their own arrival and service rate. We assume Poisson arrival processes and exponentially distributed service times. We derive an approximate method to estimate the steady state probabilities with an approximation error that can be made as small as desired at the expense of some more numerical matrix iterations. Based on these probabilities, we can derive approximations for a wide range of relevant performance characteristics, such as the expected postponement time for each item class and the first and second moment of the number of items of a certain type in the system. We illustrate our method with some numerical examples. Comparison to simulation results shows that with a moderate number of matrix iterations (~20) we can estimate key performance measures, such as the mean and variance of the num...
Analysis of Priority Queuing Models: L - R Method
Annals of pure and applied mathematics, 2017
Priority queuing models have a wide range of application in computer network system. In this paper the performance measures of fuzzy priority queuing model are computed using L-R method. L-R method is convenient and flexible compared to other methods. Numerical illustration is given to check the validity of the proposed method.
Performance Analysis of Two Priority Queuing Systems in Tandem
American Journal of Operations Research, 2012
In this paper, we consider a tandem of two head-of-line (HOL) non-preemptive priority queuing systems, each with a single server and a deterministic service-time. Two classes of traffic are considered, namely high priority and low priority traffic. By means of a generating function approach, we present a technique to derive closed-form expressions for the mean buffer occupancy at each node and mean delay. Finally, we illustrate our solution technique with some numerical examples, whereby we illustrate the starvation impact of the HOL priority scheduling discipline on the performance of the low-priority traffic stream. Our research highlights the important fact that the unfairness of the HOL priority scheduling becomes even more noticeable at the network level. Thus this priority mechanism should be used with caution.
Applied Mathematics, 2011
We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.
Average waiting time of customers in an M/D/k queue with nonpreemptive priorities
Computers & Operations Research, 1998
Scope and Purpose----Multiserver priority queues are encountered in the design of computer networks, manufacturing systems and transportation networks. Of special importance is their application in the design of Asynchronous Transfer Mode (ATM) networks. Analysis of such queues is known to be complex. The purpose of this paper is to provide a method of analysis for a multiserver priority queue with deterministic service time.
A semi-preemptive priority scheduling discipline: Performance analysis
European Journal of Operational Research, 2013
In this paper, we present an in-depth analytical study of a semi-preemptive priority scheduling discipline. This discipline eliminates the deficits of both the full-and non-preemptive versions. Under the nonpreemptive category, in particular, higher-priority customers may have to wait even when the service of a lower-priority customer has just started, while under the full-preemptive discipline, the almost completed service of a lower-priority customer may be interrupted due to the arrival of higher-priority customers, possibly causing a large extra delay. For fixed low-priority service times, the semi-preemptive priority scheduling discipline shows a performance gain of up to 6% compared to the full-and nonpreemptive versions.
Modeling and Performance Evaluation of Multi-Class Queuing System with QoS and Priority Constraints
Electronics, 2021
Many service providers often categorize their users into multi-classes, depending on their service requirements. Each class has strict quality of service (QoS) demands (e.g., minimum required service rate or transfer time) that must be ensured throughout its service. In some cases, priorities are also assigned in a multi-class user’s environment to ensure that the important class user shall be serviced first. In this paper, we have developed a novel Markov chain based analytical model to investigate and evaluate a multi-class queuing system with a strict QoS requirement and priority constraints. Experimental analysis is conducted for two users classes, i.e., class-1 (may be free/student users) and class-2 (may be paid/research users). Each class requests have strict QoS requirements in terms of the minimum required rate (MRR) that must be ensured throughout its lifetime once the request is admitted into the system. Secondly, class-2 requests have preemption priority over class-1, i....
Multi-Server Queueing Systems with Multiple Priority Classes
Queueing Systems, 2005
We present the first near-exact analysis of an M/PH/k queue with m > 2 preemptive-resume priority classes. Our analysis introduces a new technique, which we refer to as Recursive Dimensionality Reduction (RDR). The key idea in RDR is that the m-dimensionally infinite Markov chain, representing the m class state space, is recursively reduced to a 1-dimensionally infinite Markov chain, that is easily and quickly solved. RDR involves no truncation and results in only small inaccuracy when compared with simulation, for a wide range of loads and variability in the job size distribution.
A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities
Mathematics, 2020
A single-server queueing system with a finite buffer, several types of impatient customers, and non-preemptive priorities is analyzed. The initial priority of a customer can increase during its waiting time in the queue. The behavior of the system is described by a multi-dimensional Markov chain. The generator of this chain, having essential dependencies between the components, is derived and formulas for computation of the most important performance indicators of the system are presented. The dependence of some of these indicators on the capacity of the buffer space is illustrated. The profound effect of the phenomenon of correlation of successive inter-arrival times and variance of the service time is numerically demonstrated. Results can be used for the optimization of dispatching various types of customers in information transmission systems, emergency departments and first aid stations, perishable foods supply chains, etc.