Priority Classes Of Customers Research Articles

Resource Availability Modeling and Optimization in a Car Park Management Problem

This paper addresses the modeling and optimization of resource availability in car parks, serving different priority classes of customers. The authors examine various formulations of the problem concerning two general objectives: a) increasing the availability for high priority customers and b) maximizing the aggregate service level. In the current context, priority classes are specified according to different space reservation options provided by the parking management company (monthly parking, hourly parking, parking on demand, etc.). Based on actual historical traffic data and under certain methodological assumptions, they calculate the arrival and service rates for each class of customers. These are subsequently used as inputs in a Markov model that describes the evolution of the number of free parking spaces in time, given that some spaces are reserved for higher priority classes. Optimization techniques and OR heuristics are applied to deal with numerical aspects of the associated reservation planning issues.

Waiting Time Distributions in the Preemptive Accumulating Priority Queue

We consider a queueing system in which a single server attends to N priority classes of customers. Upon arrival to the system, a customer begins to accumulate priority linearly at a rate which is distinct to the class to which it belongs. Customers with greater accumulated priority levels are given preferential treatment in the sense that at every service selection instant, the customer with the greatest accumulated priority level is selected next for servicing. Furthermore, the system is preemptive so that the servicing of a customer is interrupted for customers with greater accumulated priority levels. The main objective of the paper is to characterize the waiting time distributions of each class. Numerical examples are also provided which exemplify the true benefit of incorporating an accumulating prioritization structure, namely the ability to control waiting times.

Analysis of a queue with two priority classes and feedback controls

In this paper, a queueing system with two priority classes of customers is investigated. In the queueing system, customers of high priority can preempt the service of customers of low priority. Customers can wait in buffers of finite size. A congestion control mechanism is proposed to model various practical problems. The steady-state probabilities are computed with the help of the framework of quasi-birth–death processes using the theory of generalized invariant subspace. Performance measures of interest are also derived and demonstrated by numerical results.

How many servers are best in a dual-priority [formula omitted] system?

We ask the question, “for minimizing mean response time (sojourn time), which is preferable: one fast server of speed 1, or k slow servers each of speed 1 / k ?” Our setting is the M / PH / k system with two priority classes of customers, high priority and low priority, where PH is a phase-type distribution. We find that multiple slow servers are often preferable, and we demonstrate exactly how many servers are preferable as a function of the load and service time distribution. In addition, we find that the optimal number of servers with respect to the high priority jobs may be very different from that preferred by low priority jobs, and we characterize these preferences. We also study the optimal number of servers with respect to overall mean response time, averaged over high and low priority jobs. Lastly, we ascertain the effect of the service demand variability of high priority jobs on low priority jobs.

A Spectral Method for a Nonpreemptive Priority BMAP/G/1 QUEUE

In this paper we consider a nonpreemptive priority queue with two priority classes of customers. Customers arrive according to a batch Markovian arrival process (BMAP). In order to calculate the boundary vectors we propose a spectral method based on zeros of the determinant of a matrix function and the corresponding eigenvectors. It is proved that there are M zeros in a set Ω, where M is the size of the state space of the underlying Markov process. The zeros are calculated by the Durand-Kerner method, and the stationary joint probability of the numbers of customers of classes 1 and 2 at departures is derived by the inversion of the two-dimensional Fourier transform. For a numerical example, the stationary probability is calculated.

Priority queue with two-state Markov-modulated arrivals

The authors consider a single server priority queueing system with two priority classes of customers. The work is motivated for performance analysis of multiplexing video and data in communication networks, where videos at cell level arrive according to a two-state Markov-modulated Poisson process (MMPP) and data arrive according to a Poisson process. With the supplementary variable method, the authors explicitly obtain the steady-state joint generating function of the queue lengths of each class. They also investigate the queue lengths of each class by a technique of Markov-modulated fluid flow (MMFF). In comparison with the MMPP model, the MMFF model provides computationally simple procedures and results. Numerical results show that performance measures obtained with the MMFF model are quite close to those with the MMPP model.

Pseudo-conservation law for a priority polling system with mixed service strategies

In this paper we consider a discrete-time cyclic-service system consisting of multiple stations visited by a single server. Several priority classes of customers arrive at each station according to independent batch Bernoulli processes. The head-of-the-line (HL) priority rule and non-zero switch-over times between stations are assumed. The customers are served at each station under a mixed (exhaustive, gated, and 1-limited) service strategy. We obtain an exact expression for a weighted sum of the mean waiting times for the individual priority classes, a so-called pseudo-conservation law. A continuous-time result is derived as a special case of our model.

An n-class structured priority queue with vacations

We consider a queue with batch arrivals, accepting n priority classes of customers. The arrival process is Poisson; the service times have a general distribution, common within each class. The server takes multiple vacations each time the system becomes empty. The Laplace transforms of the joint distributions of the system states and the elapsed or remaining service (or vacation) time are obtained for the transient regime and for steady state. They are used to study the amount of unfinished work in the system

Analysis of a nonpreemptive priority queue with SPP arrivals of high class

This paper considers a nonpreemptive priority queueing system with two priority classes of customers, where high priority customers arrive to the system in accordance with a switched Poisson process ( SPP) and low priority customers in accordance with a Poisson process. Using the supplementary variable technique, we derive the joint probability generating function of the stationary queue length distributions and the Laplace-Stieltjes transforms of the stationary waiting time distributions of high and low priority customers. We also present some numerical results in order to show the computational feasibility of the analytical results.

Strong approximations for priority queues; head-of-the-line-first discipline

In this paper, we obtain strong approximation theorems for a single server queue withr priority classes of customers and a head-of-the-line-first discipline. By using priority queues of preemptive-resume discipline as modified systems, we prove strong approximation theorems for the number of customers of each priority in the system at timet, the number of customers of each priority that have departed in the interval [0,t], the work load in service time of each priority class facing the server at timet, and the accumulated time in [0,t] during which there are neither customers of a given priority class nor customers of priority higher than that in the system.

Service Constrained (s, S) Inventory Systems with Priority Demand Classes and Lost Sales

This paper presents a model of an (s, S) inventory system in which there are two priority classes of customers. The model treats excess demands as lost sales and can accommodate an arbitrary deterministic lead time. After considering the associated Markov-chain model, an approximate, renewal-based model is derived. This approximation is used to develop a greedy heuristic which minimizes expected costs subject to a fill-rate service constraint. The paper concludes with the results of an extensive numerical test of both the accuracy of the approximation and the performance of the heuristic with respect to the true optimal solution. Results indicate good performance which deteriorates as the fill rate requirement and lead time increase.

A Single Server Queueing System Working under Mixed Priority Disciplines

A single server dispenses service to m priority classes of customers. The arrival process of the ith class, i = 1, 2, …, m, is a homogeneous Poisson distribution. Service times of each class are independent identical arbitrarily distributed random variables with a finite second moment. The smaller the index of a class, the higher its priority degree. For i < j, class i has preemptive priority over j if and only if (iff) j − i > d, and nonpreemptive priority otherwise, where d is a predetermined non-negative integer. Within each priority class the FIFO service rule is obeyed. Setup activities take place before starting or resuming service. An interrupted service is resumed when the system contains no customers with preemptive priority. The preemptive regimes considered are resume and repeat with and without resampling. For each of the mixed disciplines the steady state Laplace-Stieltjes transforms and the expectations of the waiting time and the time in the system are calculated for a k customer (k = 1, 2, …, m). Guidelines for minimization of the system's expected operating cost per unit time with respect to d and to the priority assignment, are discussed. Results are illustrated by a numerical example.

Common-control queuing system with priority service

The paper presents a detailed study of a common-control delay system with non-pre-emptive priority service. The system considered in the paper has a single server and r priority classes of customers, each with a distinct independent Poisson input, but all customers have the same exponential service time. The operating time of the common control is assumed to have an exponential distribution. The stationary distribution of the number of customers or the state of the system and the Laplace transform of the waiting-time distribution are obtained.

Some Heavy-Traffic Limit Theorems for a Priority Queue with General Arrivals

This paper considers a single-server queue with two priority classes of customers. Interarrival times and service times for the two classes of customers are assumed to form four mutually independent renewal processes determined by general distributions. In two cases for which a steady state does not exist, limit theorems are obtained for the low-priority waiting time and for the total uncompleted service time of all customers in the system at time t.

A Priority Queue with Low-Priority Arrivals General

This paper considers a single-server queue with two priority classes of customers. High-priority arrivals are assumed to be Poisson, but interarrival times for low-priority customers are allowed to have a general distribution. Under either the head-of-the-line or preemptive-resume discipline, a formal solution is obtained for the Laplace-Stieltjes transform of the steady-state distribution of the low-priority waiting time. A limit theorem for the low-priority waiting time is also obtained under one heavy-traffic condition for which a steady state does not exist.

Weak convergence theorems for priority queues: preemptive-resume discipline

We shall consider a single-server queue with r priority classes of customers and a preemptive-resume discipline. In this system customers are served in order of their priority while customers of the same priority are served in order of their arrival. Higher priority customers, immediately upon arrival, replace lower priority customers at the server, while customers displaced in this way return to the server before any other customers of the same priority receive service. When a displaced customer returns to the server, his remaining service time is the uncompleted portion of his original service time (cf. Jaiswal (1968)).

Weak convergence theorems for priority queues: preemptive-resume discipline

We shall consider a single-server queue with r priority classes of customers and a preemptive-resume discipline. In this system customers are served in order of their priority while customers of the same priority are served in order of their arrival. Higher priority customers, immediately upon arrival, replace lower priority customers at the server, while customers displaced in this way return to the server before any other customers of the same priority receive service. When a displaced customer returns to the server, his remaining service time is the uncompleted portion of his original service time (cf. Jaiswal (1968)).