Nonpreemptive Priority Discipline Research Articles

Analysis of M/M/1/N Stochastic Queueing—Inventory System with Discretionary Priority Service and Retrial Facility

In this paper, we analyze a queueing–inventory system with two classes of customers, high priority (HP) and low priority (LP), under the discretionary priority discipline. The LP customers are served in two stages: preliminary service in stage-I and main service in stage-II. In contrast, HP customers require only the main service. Whenever the inventory level is less than the threshold level during the stage-I service of an LP customer, an arriving HP customer is allowed to interrupt the service of an LP customer by adopting the mixed-priority discipline. Otherwise, non-preemptive priority discipline is used in both stages. The interrupted LP customer moves to orbit and retries for the service whenever the server is free. The waiting hall of finite capacity is afforded for the HP customer only. The orbital search is provided for LP customers in orbit. The inventory is replenished following the (s,Q) ordering policy, with the lifetimes of the items being exponentially distributed. An expression for the stability condition is determined explicitly, and system performance measures are evaluated. Numerical examples are formulated for different sets of input values of the parameters.

Analysis of a MAP/PH/1 Queue with Discretionary Priority Based on Service Stages

In this paper, we study a MAP/PH/1 queue with two classes of customers and discretionary priority. There are two stages of service for the low-priority customer. The server adopts the preemptive priority discipline at the first stage and adopts the nonpreemptive priority discipline at the second stage. Such a queuing system can be modeled into a quasi-birth-and-death (QBD) process. But there is no general solution for this QBD process since the generator matrix has a block structure with an infinite number of blocks and each block has infinite dimensions. We present an approach to derive the bound for the high-priority queue length. It guarantees that the probabilities of ignored states are within a given error bound, so that the system can be modeled into a QBD process where the block elements of the generator matrix have finite dimensions. The sojourn time distributions of both high and low priority customers are obtained. Some managerial insights are given after comparing the discretionary priority rule with the preemptive and nonpreemptive disciplines numerically.

Performance Modeling of Proposed GUISET Middleware for Mobile Healthcare Services in E-Marketplaces

GUISET is a proposed middleware engine currently under study in South Africa. The goal is to provide utility services for small, medium, and macroenterprises in the context of mobile e-services. Three things are important to make this engine effective and efficient: the implementation, performance, and the pricing strategy. The literature has delved richly into implementation issue of similar projects. Both the performance and the pricing strategy issues have not been fully discussed especially in the context of mobile healthcare services. Some literature has addressed the performance issue using the exogenous nonpriority and the preemptive model. However, with providers offering different services using that approach may prove to be difficult to implement. This work extends existing and widely adopted theories to non-preemptive model by using the queuing theory and the simulation model in the context of mobile healthcare services. Our evaluation is based on non-preemptive priority and nonpriority discipline. Our results reveal that the unconditional average waiting time remains the same with reduction in waiting time over the non-preemptive priority model in four out of the five classes observed. This is envisaged to be beneficial in mobile healthcare services where events are prioritized and urgent attention is needed to be given to urgent events.

A first passage time problem for spectrally positive Lévy processes and its application to a dynamic priority queue

We study a first passage time problem for a class of spectrally positive Lévy processes. By considering the special case where the Lévy process is a compound Poisson process with negative drift, we obtain the Laplace–Stieltjes transform of the steady-state waiting time distribution of low-priority customers in a two-class M/GI/1 queue operating under a dynamic non-preemptive priority discipline. This allows us to observe how the waiting time of customers is affected as the policy parameter varies.

Scheduling policies in the M/G/1 make-to-stock queue

In this paper, we analyse a production/inventory system modelled as an M/G/1 make-to-stock queue producing different products requiring different and general production times. We study different scheduling policies including the static first-come-first-served, preemptive and non-preemptive priority disciplines. For each static policy, we exploit the distributional Little's law to obtain the steady-state distribution of the number of customers in the system and then find the optimal inventory control policy and the cost. We additionally provide the conditions under which it is optimal to produce a product according to a make-to-order policy. We further extend the application area of a well-known dynamic scheduling heuristic, Myopic(T), for systems with non-exponential service times by permitting preemption. We compare the performance of the preemptive-Myopic(T) heuristic alongside that of the static preemptive-bμ rule against the optimal solution. The numerical study we have conducted demonstrates that the preemptive-Myopic(T) policy is superior between the two and yields costs very close to the optimal.

Loss performance model for wireless channels with autocorrelated arrivals and losses

In this paper, we firstly propose simple and computationally efficient wireless channel modeling algorithm that explicitly takes into account first- and second-order statistics of frame error observations. For this purpose we use a discrete-time Markov modulated process with at most single event (error) at any time slot. Then, we identify a class of priority queuing systems of G + G/GI/1/K type capable to model the frame transmission process over wireless channels with correlated arrival and loss processes. Using the proposed frame error process, performance evaluation model of the wireless channel at the data-link layer is then reduced to the special case of ∑ i D-BMAP i /D/1/K queuing system with non-preemptive priority discipline. The proposed queuing representation allows to capture forward error correlation (FEC) and automatic repeat request (ARQ) functionality of the data-link layer as well as distributional and autocorrelational properties of the frame arrival and frame loss processes. This model is further analyzed for a number of performance parameters of interest including probability function of the number of frames in the system and probability function of the number of lost frames. It is shown that the channel response in terms of the mean number of frames in the system and the mean number of lost frames varies substantially for different first- and second-order frame error and arrival statistics. The impact of input statistics is also different for normal ( ρ < 1) and overloaded conditions ( ρ ⩾ 1) of ∑ i D-BMAP i /D/1/K queuing system.

An Exact Analysis of the Multi‐class M/M/k Priority Queue with Partial Blocking

We consider a multi‐server queuing model with two priority classes that consist of multiple customer types. The customers belonging to one priority class customers are lost if they cannot be served immediately upon arrival. Each customer type has its own Poisson arrival and exponential service rate. We derive an exact method to calculate the steady state probabilities for both preemptive and nonpreemptive priority disciplines. Based on these probabilities, we can derive exact expressions for a wide range of relevant performance characteristics for each customer type, such as the moments of the number of customers in the queue and in the system, the expected postponement time and the blocking probability. We illustrate our method with some numerical examples.

Smoothed Perturbation Analysis for Single-Server Queues by Some General Service Disciplines

We consider some single-server queues with general service disciplines, where the family of the queueing processes are parameterized by the service time distributions. Through the smoothed perturbation analysis (SPA) technique, we present under some mild conditions a unified approach to give the strongly consistent estimator for the gradient of the steady-state mean sojourn time with respect to the parameter of service time distributions, provided that it exists. Although the implementation of the SPA requires the additional sub-paths in general, the derived estimator is given as suitable for single-run computation. Simulation results are presented for queues with non-preemptive and preemptive-resume priority disciplines which demonstrate the performance of our estimators.

Smoothed Perturbation Analysis for Single-Server Queues by Some General Service Disciplines

We consider some single-server queues with general service disciplines, where the family of the queueing processes are parameterized by the service time distributions. Through the smoothed perturbation analysis (SPA) technique, we present under some mild conditions a unified approach to give the strongly consistent estimator for the gradient of the steady-state mean sojourn time with respect to the parameter of service time distributions, provided that it exists. Although the implementation of the SPA requires the additional sub-paths in general, the derived estimator is given as suitable for single-run computation. Simulation results are presented for queues with non-preemptive and preemptive-resume priority disciplines which demonstrate the performance of our estimators.

Differential service in high-speed interconnection systems: an algorithm for prioritized access

The requirement to connect high-performance components of supercomputer systems has caused an increasing demand for connection-oriented, high-speed communication in a peer-to-peer environment. The importance of this type of communication is underscored by the advent of the high-performance parallel interface (HIPPI) standard, designed to support the commercial development of interconnection systems for this environment. For such interconnection systems, we present a connection management algorithm that supports priorities to provide preferential access for important classes of traffic, and that assures equitable access for all connections within the same priority class. At the same time, the algorithm utilizes the connection resources efficiently and assures low overhead at the nodes. We demonstrate the algorithm's applicability by outlining a centralized as well as a distributed implementation in an HIPPI-based interconnection system. Furthermore, we introduce an analytic priority model that can be used to evaluate an interconnection system's performance under the algorithm. Using this model, we analyze the efficacy of the nonpreemptive priority discipline and show the load/throughput behavior of a typical system.

Performance analysis of input and output queueing packet switch with multiple priority classes

AbstractThis paper proposes an N X N input‐output buffered switch model which switches several kinds of packets emphasizing the real‐time property as well as packets emphasizing the secure transmission. The model corresponds to the Poisson and Bernoulli traffic switching system. Such performances as the average system queueing delay and the loss probability for the packet emphasizing the real‐time transmission are analyzed. Nonpreemptive priority discipline is applied on the input side where the circuit configuration is relatively simple. On the output side, the first‐come/first‐served (FCFS) process is applied without considering the priority service.In the proposed model, the output buffer size is assumed as finite and the input buffer size is assumed as infinite. For the two kinds of switching systems which serve the Poisson arrival packets and the Bernoulli arrival packets, respectively, the mean system queueing delay for the priority class is analyzed. For the case where the input buffer size is limited for the packet with a high priority emphasizing the real‐time transmission, the relation between the loss probability for the packet with a high priority and the sizes of the input and output buffers is investigated by a computer simulation for the case of two classes. The adequate input buffer size for the packet with a high priority is determined.

Approximate analysis for heterogeneous multiprocessor systems with priority jobs

This paper presents an approximate analysis for a heterogeneous multiprocessor system with preemptive and nonpreemptive priority discipline. Each job is dispatched to a processor according to a predetermined algorithm. The approximation technique is based both on the lumping of system states and on an independent assumption. By lumping a set of states into a superset, the laborious work of generating balance equations is simplified, and computation time becomes insignificant. The mean response time for each job class obtained by the approximations is numerically compared with exact analysis and simulation results. Comparisons in the preemptive case show that the difference between approximation and simulation is within 10% in models handling single and two classes and is 10% on a average in the models with three classes. In the nonpreemptive case, it is within 10%. A numerical comparison of the preemptive and nonpreemptive models is also shown.

Message delays at packet-switching nodes serving multiple classes

A packet-switching node is modeled as a single-server queueing system. Messages in class c have J/sub c/ packets, each of which has a length which may be drawn from a general service time distribution prescribed on the basis of the packet's position in the message. All of the messages' packets arrive at the instant of message arrival; each packet within the message has a preassigned priority. The first packet of the message joins a transmission queue at the message arrival instant, there being one queue for each distinct priority. Upon completion of transmission of a given packet within a message, its successor packet joins the queue of appropriate priority. Packets which are waiting in the queues are serviced by the trunk under a nonpreemptive priority discipline. A method is presented for finding average message system times for the service discipline just described. This class of service disciplines includes several service disciplines which have been reported in the literature including the PR+RR, the HOL, and HOLP, the RR, and others that are discussed herein. Some numerical examples are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Interdeparture times in M/G/1 queueing systems with non-preemptive priority discipline

This paper proposes exact and/or approximate formulae for the Laplace-Stieltjes transforms of interdeparture time distributions in M/G/1 systems with non-preemptive priority discipline. These formulae are intended mainly for two-moment approximations in the context of computer models of queueing networks. The predictive value of the approximate ones is validated by simulation.

A priority M/G/1 queue with application to voice/data communication

A single server queue, with two types of customers having different Poisson arrival rates and different general service distributions, is considered in which only one type of customer can be buffered. The customers that cannot be buffered are assumed to have preemptive priority over the other customers. The customers that can be buffered belong to several priority classes in which service is provided according to a non-preemptive priority discipline among the classes. The Laplace-Stieltjes transform of the queueing and system times for different priority classes and some resulting performance measures are obtained using level crossing methods. This model has applications to integrated voice/data transmission and to systems where the service medium is subject to breakdowns.

Analysis of common memory access contention with nonpreemptive priority oiscipline

AbstractMultiprocessor controlled electronic switching systems suffer from performance degradation due to common memory access contention. Therefore, there have been many studies on the common memory access contention. However, most of them deal with the case of equal access rate. This paper considers common memory access contention in multiprocessor controlled switching systems, in which one of the processors, called MCP, has a different common memory access rate than the other processors, called CPs. In this multiprocessor system, common memory access requests are served according to non‐preemptive priority discipline based on the processor type. This common memory access contention is modeled as a finite source queueing system with nonpreemptive priority discipline. The model is analyzed and the effect of nonpreemptive priority discipline on system performance (number of instruction steps executed) is evaluated, compared with the ordinary FIFO discipline.

On a single-server queue with multiple transaction

An algorithm is presented to determine time-dependent as well as several stationary queue length characteristics for single-server queues, in which the service transaction can consist of two components: the normal service time and the post-service time, In particular, a component wise non-preemptive priority discipline is considered, where the customers waiting for receiving their normal service time are preferred in face of the customers waiting for receiving their post-service time. The stationary characteristics of the total number of customers are obtained by solving a system of relationships between them where only one fixed stationary characteristic must be calculated explicitly.

Finite capacity priority queues with potential health applications

The queuing processes of interest in this paper are that of waiting lines with two priorities and multiple service channels. The arrival process is assumed Poison and the service time distribution is negative exponential. Arriving units enter service if there is at least one idle channel, otherwise they join a finite queue and are served according to a non-preemptive priority discipline. If a low priority arriving unit finds the queue full, it is not allowed to enter the system and is considered “blocked” or lost. In the first model a high priority arrival may displace a low priority unit from the full queue and may be “blocked” if the queue consists of high priority units only. In the second model the high priority unit may still displace a low priority unit from the full queue but it will never be “blocked” and may wait “outside” the system if the system is full. Thus far there has been no discussion of such models in queuing theory literature. In this paper analytical expressions for average waiting times have been obtained for the two models. Two potential applications of the models are described and the usefulness of the models is illustrated by numerical examples.

Message Delays for TDMA Scheme Under a Nonpreemptive Priority Discipline

A TDMA access-control scheme operating under a nonpreemptive message-based priority discipline is considered and analyzed. The moment generating function (MGF) of the message waiting-time is obtained, at an arbitrary station of the network, under the assumptions of a Poisson message arrival stream and random message lengths governed by a general distribution, for each priority class. Using these results, explicit formulas for any moment of the message delay can be obtained. In particular, expressions for the average and standard deviation of the message waiting-time are presented, for the case when short (e.g., interactive) messages have priority over longer (e.g., batch) messages.

Nonpreemptive Priority Queue with Binomial Input

In our queue model of nonpreemptive priority discipline, we assume that arrivals occur at discrete time points, follow binomial distribution, and have a discrete time service distribution. In the limit, it is shown that all the parameters of the resulting queue, with the above arrival and service pattern, agree with those derived already by various authors, except for different notations used for service and arrival rates. At the end of this paper, this discipline is compared with that of the “first-come-first-served” discipline and the effect of priorities on average waiting time is obtained.