Non-preemptive Priority Research Articles

Sufficient ergodicity conditions for queueing systems with non-preemptive priority

Sufficient ergodicity conditions for queueing systems with non-preemptive priority

Retrial Queuing System with Randomized Push-Out Mechanism and Non-Preemptive Priority

A single-server retrial queueing system with finite buffer size, Poisson arrivals, an exponentially distributed service time is considered. If an arriving customer finds the queue completely occupied, it joins a special retrial waiting group (named orbit) in order to seek service over again after some period of time which have exponential distribution. The primary customers take non-preemptive priority over secondary customers. We also introduce so-called randomized push-out buffer management mechanism. It allows you push secondary customers out of the system to free up space that could be taken by primary customers. It is shown that such a queueing system can be reduced to analogous model without retrials. Using generating function technique, the loss probabilities for both types of customers are obtained. Theoretical results allow to investigate the dependency of loss probabilities on the main model parameters (like push-out and retrial probabilities). Special areas of loads are found, where the model locks itself up for secondary customers or follows linear loss law as well. A detailed comparison is made with the case of preemptive priority, which was studied by the authors earlier.

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.

Performance evaluation and analysis of a discrete queue system with multiple working vacations and non-preemptive priority

In this paper, we introduce a discrete time Geo/Geo/1 queue system with non-preemptive priority and multiple working vacations. We assume that there are two types of customers in this queue system named Customers of type-Ⅰ and Customers of type-Ⅱ. Customer of type-Ⅱ has a higher priority with non-preemption than Customer of type-Ⅰ. By building a discrete time four-dimensional Markov Chain which includes the numbers of customers with different priorities in the system, the state of the server and the service state, we obtain the state transition probability matrix. Using a birth-and-death chain and matrix-geometric method, we deduce the average queue length, the average waiting time of the two types of customers, and the average busy period of the system. Then, we provide some numerical results to evaluate the effect of the parameters on the system performance. Finally, we develop some benefit functions to analyse both the personal and social benefit, and obtain some optimization results within a certain range.

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.

Performance analysis of a discrete-time <inline-formula><tex-math id="M1">$ Geo/G/1$</tex-math></inline-formula> retrial queue with non-preemptive priority, working vacations and vacation interruption

This paper is concerned with a discrete-time $ Geo/G/1$ retrial queueing system with non-preemptive priority, working vacations and vacation interruption where the service times and retrial times are arbitrarily distributed. If an arriving customer finds the server free, his service commences immediately. Otherwise, he either joins the priority queue with probability $ α$, or leaves the service area and enters the retrial group (orbit) with probability $ \mathit{\bar{\alpha }}\left( = 1-\alpha \right)$. Customers in the priority queue have non-preemptive priority over those in the orbit. Whenever the system becomes empty, the server takes working vacation during which the server can serve customers at a lower service rate. If there are customers in the system at the epoch of a service completion, the server resumes the normal working level whether the working vacation ends or not (i.e., working vacation interruption occurs). Otherwise, the server proceeds with the vacation. Employing supplementary variable method and generating function technique, we analyze the underlying Markov chain of the considered queueing model, and obtain the stationary distribution of the Markov chain, the generating functions for the number of customers in the priority queue, in the orbit and in the system, as well as some crucial performance measures in steady state. Furthermore, the relation between our discrete-time queue and its continuous-time counterpart is investigated. Finally, some numerical examples are provided to explore the effect of various system parameters on the queueing characteristics.

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.

Blended call center with idling times during the call service

ABSTRACTWe consider a blended call center with calls arriving over time and an infinitely backlogged amount of outbound jobs. Inbound calls have a non-preemptive priority over outbound jobs. The inbound call service is characterized by three successive stages where the second one is a break; i.e., there is no required interaction between the customer and the agent for a non-negligible duration. This leads to a new opportunity to efficiently split the agent time between inbound calls and outbound jobs. We focus on the optimization of the outbound job routing to agents. The objective is to maximize the expected throughput of outbound jobs subject to a constraint on the inbound call waiting time. We develop a general framework with two parameters for the outbound job routing to agents. One parameter controls the routing between calls and the other performs the control inside a call. We then derive structural results with regard to the optimization problem and numerically illustrate them. Various guidelines to call center managers are provided. In particular, we prove for the optimal routing that at least one of the two outbound job routing parameters has an extreme value.

Non-preemptive priority scheduler with multiple thresholds for network routers

Non-preemptive priority scheduler with multiple thresholds for network routers

An analysis on Kendall Lee queueing system with non-preemptive priority at BRI Ahmad Dahlan Yogyakarta

This research was aimed to determine the Kendall Lee model, measure the Performances and analyze the optimal condition of queue at tellers line at BRI Unit K.H Ahmad Dahlan Yogyakarta. First, the model was constructed based on Kendall Lee in which the parameter values were obtained from the fitness test of the data distribution. Next, the Performances measurements were counted using Little's Formula while the optimal condition was hold based on the total cost. Since the addition of the number of servers will influence the total cost, the optimal condition is reached for a number of servers with lowest total cost and satisfying steady state condition. The result shows that the queue system in teller counter at BRI Ahmad Dahlan Yogyakarta uses M/M/2 model with non-preemptive service distribution. The optimum number of the server due to its total cost was found to be two servers. By these, it could be concluded that the system has been using optimal condition.

Customer equilibrium in a single-server system with virtual and system queues

Consider a non-preemptive M/M/1 system with two first-come first-served queues, virtual (VQ) and system (SQ). An arriving customer who finds the server busy decides which queue to join. Customers in the SQ have non-preemptive priority over those in the VQ, but waiting in the SQ is more costly. We study two information models of the system. In the unobservable model, customers are notified only whether the server is busy, and in the observable model they are also informed about the number of customers currently waiting in the SQ. We characterize the Nash equilibrium of joining strategies in the two models and demonstrate a surprising similarity of the solutions.

The booking problem of a diagnostic resource with multiple patient classes and emergency interruptions

CT department is an appointment based service system. All patients except emergency patients should be scheduled in advance. Regular patients arrive on time. Emergency patients arrive randomly and get non-preemptive priority. So the direct waiting time of regular patients should be explicitly described. The unit direct waiting cost gradually increases with the previous waiting time. On the one hand, too many regular patients will increase the direct waiting cost for them and overtime cost for medical resources. On the other hand, too few regular patients will cause idling of medical resources and penalty for delaying regular patients’ requests. So a reasonable reservation level should be determined in advance. The booking problem is modeled as a finite horizon Markov decision process. Some booking limit structures are given to improve the total expected reward. The numerical analysis shows that our policies are much better than the policy currently employed.

A single server fuzzy queues with priority and unequal service rates

This article presents to develop a new mathematical model to construct membership functions of the fuzzy single channel queueing model F(M1, M2)/F(M1, M2)/1/PR-NP with two class of non-preemptive priority with unequal service rates. The main idea of this article is to merge between mathematical programming technique and Yager's ranking method by using α-cut approach and Zadeh extension principle to transform fuzzy queues into a family of conventional crisp (distinct) queues in this context. A numerical example is given to explain the validity of this new approach to obtain real exact values under different levels of α in the system.

Fuzzy Based Dynamic Packet Priority Determination and Queue Management method For Wireless Sensor Network

Wireless sensor networks are made up of large number of resource-constrained sensor nodes. Scheduling of different types of packets at sensor nodes is of crucial importance to reduce sensors' energy consumption, end-to-end data transmission delays and packet loss. Majority of the existing packet scheduling algorithms such as first come first serve (FCFS), preemptive priority scheduling and non-preemptive priority scheduling are not adaptive to changes in the data traffic. They also have more processing overhead and large communication delays. We propose fuzzy-based dynamic packet priority determination and queue management mechanism. In the proposed scheme, each node determines priority of packets dynamically and queues them accordingly. The proposed scheme increases fairness in scheduling and the energy efficiency by delivering the packets before their expiry. The results demonstrate that this enhanced approach outperforms FCFS and dynamic multilevel priority queue scheduling algorithms in terms of throughput, end-to-end delay and average residual energy.

A single server fuzzy queues with priority and unequal service rates

This article presents to develop a new mathematical model to construct membership functions of the fuzzy single channel queueing model F(M1, M2)/F(M1, M2)/1/PR-NP with two class of non-preemptive priority with unequal service rates. The main idea of this article is to merge between mathematical programming technique and Yager's ranking method by using α-cut approach and Zadeh extension principle to transform fuzzy queues into a family of conventional crisp (distinct) queues in this context. A numerical example is given to explain the validity of this new approach to obtain real exact values under different levels of α in the system.

Cognitive radio networks with multiple secondary users under two kinds of priority schemes: Performance comparison and optimization

In this paper, we consider a cognitive radio network with multiple Secondary Users (SUs). The SU packets generated from the SUs are divided into SU1 packets and SU2 packets, and the SU1 packets have higher priority than the SU2 packets. Different from the conventional preemptive priority scheme (called Scheme Ⅰ), we propose a non-preemptive priority scheme for the SU1 packets (called Scheme Ⅱ) to guarantee the transmission continuity of the SU2 packets. By constructing a three-dimensional Markov chain, we give the transition probability matrix of the Markov chain, and obtain the steady-state distribution of the system model. Accordingly, we derive some performance measures, such as the channel utilization, the blocking probability of the SU1 packets, the interruption probability of the SU1 packets and the SU2 packets, the normalized throughput of the SU1 packets, and the average latency of the SU2 packets. Moreover, we provide numerical experiments to compare different performance measures between the two priority schemes. Finally, we show and compare the Nash equilibrium strategy and the socially optimal strategy for the SU2 packets between Scheme Ⅰ and Scheme Ⅱ.

Automating selection of optimal packet scheduling during VоIP-traffic transmission

The usage of various packet scheduling disciplines in computer networking devices as a mechanism to ensure the quality of service is described. Stages for selection of necessary parameters values of packet scheduling during VoIP-traffic transmission in computer networks are defined. VoIP-traffic was set as a research object because there are strict requirements of VoIP-applications to the network transmission parameters. With the aid of training and experimental simulation system the numerous experiments for parameters selection of the most common packet scheduling disciplines were carried out (FIFO, WFQ, non-preemptive priority queueing). The example that illustrates the ability to adjust the weighting coefficients of WFQ packet scheduling discipline is presented. Approximate analytical dependences are obtained and they will significantly reduce system administrators’ efforts to assess and modify the parameters of packet scheduling in network devices. A method of automating selection of the optimal packet scheduling discipline is formulated.

A Queueing Theoretic Approach to Set Staffing Levels in Time‐Dependent Dual‐Class Service Systems*

ABSTRACTThis article addresses the optimal staffing problem for a nonpreemptive priority queue with two customer classes and a time‐dependent arrival rate. The problem is related to several important service settings such as call centers and emergency departments where the customers are grouped into two classes of “high priority” and “low priority,” and the services are typically evaluated according to the proportion of customers who are responded to within targeted response times. To date, only approximation methods have been explored to generate staffing requirements for time‐dependent dual‐class services, but we propose a tractable numerical approach to evaluate system behavior and generate safe minimum staffing levels using mixed discrete‐continuous time Markov chains (MDCTMCs). Our approach is delicate in that it accounts for the behavior of the system under a number of different rules that may be imposed on staff if they are busy when due to leave and involves explicitly calculating delay distributions for two customer classes. Ultimately, we embed our methodology in a proposed extension of the Euler method, coined Euler Pri, that can cope with two customer classes, and use it to recommend staffing levels for the Welsh Ambulance Service Trust (WAST).

On a general mixed priority queue with server discretion

ABSTRACTWe consider a single-server queueing system which attends to N priority classes that are classified into two distinct types: (i) urgent: classes which have preemptive resume priority over at least one lower priority class, and (ii) non-urgent: classes which only have non-preemptive priority among lower priority classes. While urgent customers have preemptive priority, the ultimate decision on whether to interrupt a current service is based on certain discretionary rules. An accumulating prioritization is also incorporated. The marginal waiting time distributions are obtained and numerical examples comparing the new model to other similar priority queueing systems are provided.

Stability property of clouds and cooperative scheduling policies on multiple types of resources in cloud computing

Cloud computing provides users a shared pool of configurable computing resources. In this paper, a cloud computing system is regarded as a queuing system, where users arrive according to a stochastic process and request resources, including CPU, memory, storage space. etc. To improve the utilization of the system under stable state, we provide some theoretical results about the relationship between the utilization and the stability of the cloud computing system. The conditions for the system to be stable are given for systems with preemptive priority and non-preemptive priority, respectively. Given the stability conditions, we suggest a scheduling algorithm to improve the optimal utilization of the could computing system with preemptive priority and non-preemptive priority, respectively. Numerical results indicate that the two algorithms provide adequate performance on utilization. In addition, the influence of different parameters on the algorithm is investigated as well.