Non-preemptive Priority Service Research Articles

Lower and upper stochastic bounds for the joint stationary distribution of a non-preemptive priority retrial queueing system

Consider a single-server retrial queueing system with non-preemptive priority service, where customers arrive in a Poisson process with a rate of $\lambda_1$ for high-priority customers (class 1) and $\lambda_2$ for low-priority customers (class 2). If a high-priority customer is blocked, they are queued, while a low-priority customer must leave the service area and return after some random period of time to try again. In contrast with existing literature, we assume different service time distributions for the two customer classes. This investigation proposes a stochastic comparison method based on the general theory of stochastic orders to obtain lower and upper bounds for the joint stationary distribution of the number of customers at departure epochs in the considered model. Specifically, we discuss the stochastic monotonicity of the embedded Markov queue-length process in terms of both the usual stochastic and convex orders. We also perform a numerical sensitivity analysis to study the effect of the arrival rate of high-priority customers on system performance measures.

Analysis of an retrial queueing system with priority services, working breakdown, Bernoulli vacation, admission control and balking

A single server serves two classes of customers under non-preemptive priority service rule are studied. In addition to this working breakdown, admission control, balking and Bernoulli vacation are also investigated. Here, the customers arrive according to two independent compound Poisson processes and the service is in general distribution. Once the system gets a breakdown, the server proceeds the service at a slower speed for the current customer, after which, the repair will commence. Moreover, the server can not allow all the customers to enter into the system, there is an admission control policy to allow customers. Applying the supplementary variable technique, the Laplace transforms of time-dependent probabilities of system state are determined and further deduced the steady state results. Also, the average number of customers in the corresponding queues and the average waiting times are estimated. Finally, the numerical results are represented.

Analysis of priority queueing system with working breakdown, repair, immediate feedback and bernoulli vacation

We analyze an M[X1], M[X2]/G1,G2/1 queue with two classes of non-preemptive priority service based on working breakdown, repair, immediate feedback and Bernoulli vacation. The server may subject to random breakdown with parameter α, during high priority service (type I), then the server will complete the service for current customer at a slower service rate compared to the regular service rate. On the other hand, during low priority service (type II), it should go for repair immediately. After the completion of each high priority service, there are two choices. First, the server can go for vacation with probability θ, secondly, its serves the next customer which has the probability (1 – θ). In case of customer dissatisfaction after completion of high priority service, immediately they receive service again without joining queue with probability r, or else the customer gets an option to discard, which has a probability of (1 – r). We use the established norm, which is the corresponding steady state results for the time dependent probability generating functions. Along with that, the expected time of wait for the expected number of customers in the high and low priority queues are computed. Numerical results along with the graphical representations are shown elaborately.

Service Mechanism and Pricing Based on Fairness Preference of Customers in Queuing System

AbstractService providers often adopt the mechanism of customer classification due to the heterogeneity of customer waiting cost. However, the classification service may cause unfairness feeling of regular customers, then affect the revenue and social welfare. This paper provides the first exact analysis about the situation that service providers offer two classes of non-preemptive priority service when customer fairness perception is explicitly modeled. We model customer fairness perception as a negative utility on regular customers that’s proportional to the waiting time difference between the two queues. By analyzing a stylized M/M/1 queue in monopoly service system, we can derive important results some of which reaffirm existed research results. First, from the perspective of revenue maximization, service providers should also adopt the mechanism of customer classification and set up the two kinds of customers where they can see each other. Next, considering customer utility maximization, service providers should cancel the mechanism of customer classification, and keep one queue (regular customers) only. Then, from the perspective of social welfare maximization, service providers should also adopt the mechanism of customer classification but set up the two kinds of customers where they cannot feel each other. Finally, this paper concludes the optimal pricing based on customer classification in the above three different perspectives. This research shows important reference value and practical significance for service providers who adopt the mechanism of classification service.

Transient Analysis of $$M^{[X_{1}]},M^{[X_{2}]}/G_{1},G_{2}/1$$ M [ X 1 ] , M [ X 2 ] / G 1 , G 2 / 1 Retrial Queueing System with Priority Services, Working Vacations and Vacation Interruption, Emergency Vacation, Negative Arrival and Delayed Repair

This paper deals with the analysis of two classes of batch arrivals, one is high priority and other is low priority(retrial) customers with non-preemptive priority service, working vacations, negative arrival, emergency vacation for an unreliable server, which consists of a break-down by negative arrival and delay time to start repair. When there are no customers in the queue and in the orbit at the time of service completion for a positive customers, the server goes for a working vacation. The server works at a lower service rate during working vacation period. If there are no customers in the system at the end of vacation, the server becomes idle and ready for serving the new arrivals with probability p(single working vacation) or it remains on vacation with probability $$q=(1{-}p)$$ (multiple working vacations). Here we assume that customers arrive according to compound Poisson process in which high priority customers are assigned to class one and class two customers are of a low priority type. The priority customers that find the server busy are queued and then served in accordance with FCFS discipline. The arriving low priority customers on finding the server busy are queued in the orbit in accordance with FCFS constant retrial policy. The arrival of negative customer remove the customer being in service and makes the server breakdown and the server fail for a short interval of time. When the server fails it will send to repair. But the repair time do not start immediately, there is a delay time to start the repair process. We consider an emergency vacation which means that during the service time the server suddenly go for a vacation and the interrupted customer waits to getting the remaining service. The retrial time, service time, emergency vacation time, delay time and repair time are all follows general(arbitrary) distribution, working vacation time and negative arrival follows exponential distribution. The time dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results are obtained explicitly. Also some performance measures of our model such as the system state probabilities, reliability indices, the average number of customer in the high priority queue and the low priority in the orbit and the average waiting time are derived. Numerical results are computed and graphical representations are presented.

A Framework for Packet Delay Analysis of Point-to-Multipoint Underlay Cognitive Radio Networks

This paper presents a queueing analytical framework for the performance evaluation of the secondary user (SU) packet transmission with service differentiation in a point-to-multipoint underlay cognitive radio network. The transmit power of the SU transmitter is subject to the joint outage constraint imposed by the primary user receivers (PU-Rxs) and the SU maximum transmit power limit. The analysis considers a queueing model for secondary traffic with multiple classes, and different types of arrival and service processes under a non-preemptive priority service discipline. The SU quality of service (QoS) is characterized by a packet timeout threshold and target bit error rate. Given these settings, analytical expressions of the packet timeout probability and average transmission time are derived for opportunistic and multicast scheduling. Moreover, expressions of the average packet waiting time in the queue and the total time in the system for each class of traffic are obtained. Numerical examples are provided to illustrate the secondary network performance with respect to various parameters such as number of PU-Rxs and SU receivers, SU packet arrival process, QoS requirements, and the impact of interference from the primary network to the secondary network.

Priority queueing models for cognitive radio networks with traffic differentiation

In this paper, we present a new queueing model providing the accurate average system time for packets transmitted over a cognitive radio (CR) link for multiple traffic classes with the preemptive and non-preemptive priority service disciplines. The analysis considers general packet service time, general distributions for the channel availability periods and service interruption periods, and a service-resume transmission. We further introduce and analyze two novel priority service disciplines for opportunistic spectrum access (OSA) networks which take advantage of interruptions to preempt low priority traffic at a low cost. Analytical results, in addition to simulation results to validate their accuracy, are also provided and used to illustrate the impact of different OSA network parameters on the average system time. We particularly show that, for the same average CR transmission link availability, the packet system time significantly increases in a semi-static network with long operating and interruption periods compared to an OSA network with fast alternating operating and interruption periods. We also present results indicating that, due to the presence of interruptions, priority queueing service disciplines provide a greater differentiated service in OSA networks than in traditional networks. The analytical tools presented in this paper are general and can be used to analyze the traffic metrics of most OSA networks carrying multiple classes of traffic with priority queueing service differentiation.

M/M/1 Retrial queueing system with negative arrival under non-preemptive priority service

Consider a single server retrial queueing system with negative arrival under non-pre-emptive priority service in which three types of customers arrive in a poisson process with arrival rate λ1 for low priority customers and λ2 for high priority customers and λ3 for negative arrival. Low and high priority customers are identified as primary calls. The service times follow an exponential distribution with parameters μ1 and μ2 for low and high priority customers. The retrial and negative arrivals are introduced for low priority customers only. Gelenbe (1991) has introduced a new class of queueing processes in which customers are either positive or negative. Positive means a regular customer who is treated in the usual way by a server. Negative customers have the effect of deleting some customer in the queue. In the simplest version, a negative arrival removes an ordinary positive customer or a random batch of positive customers according to some strategy. It is noted that the existence of a flow of negative arrivals provides a control mechanismto control excessive congestion at the retrial group and also assume that the negative customers only act when the server is busy. Let K be the maximumnumber of waiting spaces for high priority customers in front of the service station. The high priorities customers will be governed by the Non-preemptive priority service. The access from the orbit to the service facility is governed by the classical retrial policy. This model is solved by using Matrix geometric Technique. Numerical study have been done for Analysis of Mean number of low priority customers in the orbit (MNCO), Mean number of high priority customers in the queue(MPQL),Truncation level (OCUT),Probability of server free and Probabilities of server busy with low and high priority customers for various values of λ1 , λ2 , λ3 , μ1 , μ2 ,σ and k in elaborate manner and also various particular cases of this model have been discussed.

A Retrial Inventory System with Non-Preemptive Priority Service

We consider a queueing-inventory system with two types of customers, say, high priority and low priority, arrive according to Poisson processes. The service times are exponentially distributed. The inventory is replenished according to an (s; S) policy and the replenishing times are assumed to be exponentially distributed. Retrial is introduced for low priority customers only. The orbiting customers compete for service by sending out signals that are exponentially distributed. The joint probability distribution of the number of customers in the waiting area, the number of customers in the orbit and the inventory level is obtained for the steady state case. Some important system performance measures in the steady state are derived. Several numerical examples are presented to illustrate the effect of the system parameters and costs on these measures.

On the fluid approximation for a multiclass queue under non-preemptive SBP service discipline

A multi-class single server queue under non-preemptive static buffer priority (SBP) service discipline is considered in this paper. Using a bounding technique, we obtain the fluid approximation for the queue length and busy time processes. Furthermore, we prove that the convergence rate of the fluid approximation for the queue length and busy time processes is exponential for large N. Additionally, a sufficient condition for stability is obtained.

Analysis of a finite buffer model with two servers and two nonpreemptive priority classes

In this paper, we analyze a finite buffer queueing model with two servers and two nonpreemptive priority service classes. The arrival streams are independent Poisson processes, and the service times of the two classes are exponentially distributed with different means. One of the two servers is reserved exclusively for one class with high priority and the other server serves the two classes according to a nonpreemptive priority service schedule. For the model, we describe its dynamic behavior by a four-dimensional continuous-time Markov process. Applying recursive approaches we present the explicit representation for the steady-state distribution of this Markov process. Then, we calculate the Laplace–Stieltjes Transform and the steady-state distribution of the actual waiting times of two classes of customers. We also give some numerical comparison results with other queueing models.

Quantum-Based Earliest Deadline First Scheduling for Multiservices

Latency-rate (LR) schedulers have shown their ability in providing fair and weighted sharing of bandwidth with an upper bound on delivery latency of packets while earliest departure first (EDF) schedulers have shown their ability in providing LR-decoupled service whereby the delivery latency of packets is not bounded by the reserved rate. However, EDF schedulers require traffic shapers to ensure flow protection. We propose quantum-based earliest deadline first scheduling (QEDF), a quantum-based scheduler that provides flow protection, throughput guarantee and delay bound guarantee for flows that require LR-coupled and LR-decoupled types of reservations. It classifies flows into time-critical (TC), jitter-sensitive (JS), and rate-based (RB) classes and uses a quality-of-service forwarding rule to determine the next packet to be serviced by the scheduler. It provides nonpreemptive priority service to TC queues. This allows LR-decoupled reservation for flows that have a low rate and intolerable delay. Packets from JS queues can be delayed by other packets if forwarding the latter will not result in the former missing its deadline. As a quantum-based scheduler, the QEDF scheduler provides throughput guarantees for RB queues. We present both analytical and simulation results of QEDF, whereby we evaluated QEDF in its deployment as a single-class as well as a multiservice scheduler

PERFORMANCE ANALYSIS OF A TWO-QUEUE MODEL WITH AN (M,N)-THRESHOLD SERVICE SCHEDULE

In this paper, we considera polling system consisting of two-parallel queues and a single server under an (M,N)-threshold nonpreemptive priority service schedule. Two thresholds M and N (0<>__-M<N) are set up in one of two queues, say, the second queue. At each epoch of service completion, the server decides which queue is to be served next according to the control level reached by the number of customers in the second queue. For the queueing model, we carry out the performance analysis by using the transform method and propose an algorithm to compute the generating functions of the stationary joint queue length distributions at service completion instants. We also determine the Laplace-Stieltjes transforms of the waiting time distributions for both queues, and obtain their mean waiting times.

Analysis of a multi-server queue with two priority classes and ( M, N)-threshold service schedule I: non-preemptive priority

In this paper, we propose an ( M, N)-threshold non-preemptive priority service schedule for a queueing system consisting of two-parallel queues and a multi-server. The arrival process for each queue is Poisson, and the service times are exponentially distributed with different means. We derive the generating functions of the stationary joint queue-length distribution, and then obtain the mean queue length and the mean waiting time for each queue.

Analysis of a multi-server queue with two priority classes and (M, N)-threshold service schedule I: non-preemptive priority

In this paper, we propose an (M, N)-threshold non-preemptive priority service schedule for a queueing system consisting of two-parallel queues and a multi-server. The arrival process for each queue is Poisson, and the service times are exponentially distributed with different means. We derive the generating functions of the stationary joint queue-length distribution, and then obtain the mean queue length and the mean waiting time for each queue.

Deterministic performance bounds in a window‐based token ring network supporting two priorities

Abstract A window‐based token ring protocol supporting two priority traffic streams is proposed. This protocol uses the window timers to limit the packet transmissions of a token holding station. The packets arriving during a window period are always transmitted before those arriving during subsequent window periods. Nonpreemptive priority service discipline is used to serve high priority packets. A call admission control policy based on delay bound is then employed to guarantee QoS such as the packet delay, delay jitter, and the packet loss‐free requirement for both priority traffic streams. Under such window‐based token ring operation and call admission control, network‐wide fairness can be achieved and the network output traffic characteristics become predictable. With these properties, we would expect that the window‐based token protocol is more appropriate for real‐time communications.

An Iterative Algorithm for a Multiple Finite-source Queueing Model with Dynamic Priority Scheduling

A multiple finite source queueing model with a single server and dynamic, non-preemptive priority service discipline is studied in this paper. The times the customers spend at the corresponding sources are exponentially distributed. The service times of the customers can follow exponential, Erlang or hyperexponential probability density function. By using results published earlier and an extension of mean value analysis, an iterative algorithm was developed to obtain approximate values of the mean waiting times in queues for the priority classes. The mean number of waiting customers and the server utilization of each class are obtained using the result of this algorithm and Little's formula. The algorithm is preferable to the earlier method, because it does not increase in complexity as the number of customer classes increases.

An Iterative Algorithm for a Multiple Finite-source Queueing Model with Dynamic Priority Scheduling

A multiple finite source queueing model with a single server and dynamic, non-preemptive priority service discipline is studied in this paper. The times the customers spend at the corresponding sources are exponentially distributed. The service times of the customers can follow exponential, Erlang or hyperexponential probability density function. By using results published earlier and an extension of mean value analysis, an iterative algorithm was developed to obtain approximate values of the mean waiting times in queues for the priority classes. The mean number of waiting customers and the server utilization of each class are obtained using the result of this algorithm and Little's formula. The algorithm is preferable to the earlier method, because it does not increase in complexity as the number of customer classes increases.

Performance analysis of an ISDN switch with distributed architecture: circuit switched calls

We have developed an approximate analytic model and a detailed simulation model to study the performance of an ISDN switch with distributed architecture. The analytic model treats the switch as a network of single server and infinite server queues with nonpreemptive priority service, general service times and batch arrivals. The simulation program is written in a distributed and modular way so as to simplify model development and debugging. Also extensive statistical techniques are employed for simulation output validation. It is observed that the analytic and the simulation models are in close agreement for the mean end-to-end delay and in moderately close agreement for the 95th percentile points of the end-to-end delay distribution. The comparisons between the analytic and the simulation models lead us to conjecture that the analytic model would be even more accurate for bigger systems with several hundred processors (where simulation models are too expensive to run). Even though the model assumes Poisson external call arrival process, it is shown that it may be applied with reasonable accuracy even when external call arrivals are non-Poisson. This is due to the fact that the composite message arrival process at a processor or transmission element tends to be close to Poisson even when the external call arrivals are non-Poisson.

A finite capacity dynamic priority queuing model

A single server queueing model with two types of arrivals is discussed under the assumptions of Poisson arrivals, (possibly different) general services and finite waiting room for each type of customer. Under a dynamic non-preemptive priority service rule, the steady state analysis of the model is performed. A number of interesting and intuitive results are obtained. In the case when the services are of phase type, implementable algorithms are developed for computing various system performance measures. The recursive computational schemes can be used interactively in the design of such queuing systems. A number of numerical examples are discussed.