Pricing surplus server capacity for mean waiting time sensitive customers

We consider a queueing model wherein the resource is shared by two different classes of customers, primary (existing) and secondary (new), under a service level based pricing contract. This contract between secondary class customers and resource manager specifies unit admission price and quality of service (QoS) offered. We assume that the secondary customers’ Poisson arrival rate depends linearly on unit price and service level offered while the server uses a delay dependent priority queue management scheme. We analyze the joint problem of optimal pricing and operation of the resource with the inclusion of secondary class customers, while continuing to offer a pre-specified QoS to primary class customers. Our analysis leads to an algorithm that finds, in closed form expressions, the optimal points of the resulting non-convex constrained optimization problem. We also study in detail the structure and the non-linear nature of these optimal pricing and operating decisions.     

Revenue-maximizing pricing and scheduling strategies in service systems with flexible customers

We propose a model of service operations systems in which customers are heterogeneous both in terms of their private delay sensitivity and flexibility. A service provider maximizes revenue through jointly optimal pricing and steady-state scheduling strategies. We provide a complete analysis for this generally intractable problem. Interestingly, when one queue accommodates a large population of impatient customers, it may be desirable to strategically idle the server in the other queue, which is a phenomenon new to the literature.     

On priority queues with impatient customers

In this paper, we study three different problems where one class of customers is given priority over the other class. In the first problem, a single server receives two classes of customers with general service time requirements and follows a preemptive-resume policy between them. Both classes are impatient and abandon the system if their wait time is longer than their exponentially distributed patience limits. In the second model, the low-priority class is assumed to be patient and the single server chooses the next customer to serve according to a non-preemptive priority policy in favor of the impatient customers. The third problem involves a multi-server system that can be used to analyze a call center offering a call-back option to its impatient customers. Here, customers requesting to be called back are considered to be the low-priority class. We obtain the steady-state performance measures of each class in the first two problems and those of the high-priority class in the third problem by exploiting the level crossing method. We furthermore adapt an algorithm from the literature to obtain the factorial moments of the low-priority queue length of the multi-server system exactly.      

A single server queue with service interruptions

In this paper we characterize the queue-length distribution as well as the waiting time distribution of a single-server queue which is subject to service interruptions. Such queues arise naturally in computer and communication problems in which customers belong to different classes and share a common server under some complicated service discipline. In such queues, the viewpoint of a given class of customers is that the server is not available for providing service some of the time, because it is busy serving customers from a different class. A natural special case of these queues is the class of preemptive priority queues. In this paper, we consider arrivals according the Markovian Arrival Process (MAP) and the server is not available for service at certain times. The service times are assumed to have a general distribution. We provide numerical examples to show that our methods are computationally feasible. This revised version was published online in June 2006 with corrections to the Cover Date.     

Analysis of a discrete-time preemptive resume priority buffer

In this paper, we analyze a discrete-time preemptive resume priority queue. We consider two classes of customers which have to be served, where customers of one class have preemptive resume priority over customers of the other. Both classes contain customers with generally distributed service times. We show that the use of probability generating functions is beneficial for analyzing the system contents and customer delays of both classes. It is shown (theoretically as well as by some practical procedures) how moments and approximate tail probabilities of system contents and customer delays are calculated. The influence of the priority scheduling discipline and the service time distributions on the performance measures is shown by some numerical examples.     

An overview of Stackelberg pricing in networks

The Stackelberg pricing problem has two levels of decision making: tariff setting by an operator, and then selection of the cheapest alternative by customers. In the network version, an operator determines tariffs on a subset of the arcs that he owns. Customers, who wish to connect two vertices with a path of a certain capacity, select the cheapest path. The revenue for the operator is determined by the tariff and the amount of usage of his arcs. The most natural model for the problem is a (bilinear) bilevel program, where the upper level problem is the pricing problem of the operator, and the lower level problem is a shortest path problem for each of the customers.     

Performance of service policies in a specialized service system with parallel servers

This paper considers a scheduling problem occurring in a specialized service system with parallel servers. In the system, customers are divided into the “ordinary” and “special” categories according to their service needs. Ordinary customers can be served by any server, while special customers can be served only by the flexible servers. We assume that the service time for any ordinary customer is the same and all special customers have another common service time. We analyze three classes of service policies used in practice, namely, policies with priority, policies without priority and mixed policies. The worst-case performance ratios are obtained for all of these service policies.     

基于分类服务机制的可预约排队系统设计和服务定价研究

采取合理有效的服务机制和服务定价是确保服务型企业持续有效运行的重要方式,服务提供商设计合理的服务策略可以使得服务收益达到最优。本文以服务可预约的排队系统为研究背景,对服务提供商分类服务机制选择和服务定价策略进行研究。通过考虑由两种服务策略下顾客之间的平均等待时间的对比和顾客等待厌恶心理参数形成的全新顾客服务效用模型,给出服务提供商在不同服务机制下的最优服务策略以及顾客市场规模对其服务策略选择的影响。研究表明,当预约顾客的市场规模相对较小时,服务提供商可以采取分类服务机制,即同时服务预约顾客和未预约顾客以增加服务收益,反之亦然。此外,预约顾客等待厌恶程度能够显著增大服务提供商的服务定价。     

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 preemptive loss priority queues with preemption distance

In a queueing system with preemptive loss priority discipline, customers disappear from the system immediately when their service is preempted by the arrival of another customer with higher priority. Such a system can model a case in which old requests of low priority are not worthy of deferred service. This paper is concerned with preemptive loss priority queues in which customers of each priority class arrive in a Poisson process and have general service time distribution. The strict preemption in the existing model is extended by allowing the preemption distance parameterd such that arriving customers of only class 1 throughp — d can preempt the service of a customer of classp. We obtain closed-form expressions for the mean waiting time, sojourn time, and queue size from their distributions for each class, together with numerical examples. We also consider similar systems with server vacations.     

Dynamic scheduling of a single-server two-class queue with constant retrial policy

We analyze the non-preemptive assignment of a single server to two infinite-capacity retrial queues. Customers arrive at both queues according to Poisson processes. They are served on first-come-first-served basis following a cost-optimal routing policy. The customer at the head of a queue generates a Poisson stream of repeated requests for service, that is, we have a constant retrial policy. All service times are exponential, with rates depending on the queues. The costs to be minimized consist of costs per unit time that a customer spends in the system. In case of a scheduling problem that arise when no new customers arrive an explicit condition for server allocation to the first or the second queue is given. The condition presented covers all possible parameter choices. For scheduling that also considers new arrivals, we present the conditions under which server assignment to either queue 1 or queue 2 is cost-optimal.     

Optimal server scheduling in nonpreemptive finite-population queueing systems

We consider a finite-population queueing system with heterogeneous classes of customers and a single server. For the case of nonpreemptive service, we fully characterize the structure of the server's optimal service policy that minimizes the total average customer waiting costs. We show that the optimal service policy may never serve some classes of customers. For those classes that are served, we show that the optimal service policy is a simple static priority policy. We also derive sufficient conditions that determine the optimal priority sequence.     

Dynamic Scheduling of a Multiclass Fluid Model with Transient Overload

We study the optimal dynamic scheduling of different requests of service in a multiclass stochastic fluid model that is motivated by recent and emerging computing paradigms for Internet services and applications. In particular, our focus is on environments with specific performance guarantees for each class under a profit model in which revenues are gained when performance guarantees are satisfied and penalties are incurred otherwise. Within the context of the corresponding fluid model, we investigate the dynamic scheduling of different classes of service under conditions where the workload of certain classes may be overloaded for a transient period of time. Specifically, we consider the case with two fluid classes and a single server whose capacity can be shared arbitrarily among the two classes. We assume that the class 1 arrival rate varies with time and the class 1 fluid can more efficiently reduce the holding cost. Under these assumptions, we characterize the optimal server allocation policy that minimizes the holding cost in the fluid model when the arrival rate function for class 1 is known. Using the insights gained from this deterministic case, we study the stochastic fluid system when the arrival rate function for class 1 is random and develop various policies that are optimal or near optimal under various conditions. In particular, we consider two different types of heavy traffic regimes and prove that our proposed policies are strongly asymptotically optimal. Numerical examples are also provided to demonstrate further that these policies yield good results in terms of minimizing the expected holding cost.     

Waiting time analysis of the multiple priority dual queue with a preemptive priority service discipline

The dual queue consists of two queues, called the primary queue and the secondary queue. There is a single server in the primary queue but the secondary queue has no service facility and only serves as a holding queue for the overloaded primary queue. The dual queue has the additional feature of a priority scheme to help reduce congestion. Two classes of customers, class 1 and 2, arrive to the dual queue as two independent Poisson processes and the single server in the primary queue dispenses an exponentially distributed service time at the rate which is dependent on the customer’s class. The service discipline is preemptive priority with priority given to class 1 over class 2 customers. In this paper, we use matrix-analytic method to construct the infinitesimal generator of the system and also to provide a detailed analysis of the expected waiting time of each class of customers in both queues.     

Expulsion and scheduling control for multiclass queues with heterogeneous servers

We consider an M/M/2 system with nonidentical servers and multiple classes of customers. Each customer class has its own reward rate and holding cost. We may assign priorities so that high priority customers may preempt lower priority customers on the servers. We give two models for which the optimal admission and scheduling policy for maximizing expected discounted profit is determined by a threshold structure on the number of customers of each type in the system. Surprisingly, the optimal thresholds do not depend on the specific numerical values of the reward rates and holding costs, making them relatively easy to determine in practice. Our results also hold when there is a finite buffer and when customers have independent random deadlines for service completion.     

Optimal scheduling policies in time sharing service systems

We consider optimal scheduling problems in a TSSS (Time Sharing Service System), i.e., a tandem queueing network consisting of multiple service stations, all of which are served by a single server. In each station, a customer can receive service time up to the prescribed station dependent upper bound, but he must proceed to the next station in order to receive further service. After the total amount of the received services reaches his service requirement, he departs from the network. The optimal policy for this system minimizes the long-run average expected waiting cost per unit of time over the infinite planning horizon. It is first shown that, if the distribution of customer's service requirement is DMRL (Decreasing Mean Residual Life), the policy of giving the highest priority to the customer with the most attained service time is optimal under a set of some appropriate conditions. This implies that any policy without interruptions and preemptions of services is optimal. If the service requirement is DFR (Decreasing Failure Rate), on the other hand, it is shown that the policy of giving the highest priority to the customer with the least attained service time, i.e., the so-called LAST (Least Attained Service Time first) is optimal under another set of some appropriate conditions. These results can be generalized to the case in which there exist multiple classes of customers, but each class satisfies one of the above sets of conditions.     

Workforce scheduling with multiple objectives

In workforce scheduling, the optimal schedule has traditionally been determined by minimizing the cost of labor subject to an acceptable service level, which is defined as the percentage of customers served within a predetermined time interval. We propose an alternative multidimensional paradigm, where cost minimization and service level maximization are considered simultaneously, together with other, complementary criteria. The ultimate goal of the proposed approach is to open a broader workforce scheduling paradigm that incorporates service quality into the analysis and provides the possibility to study the interaction between cost and service quality. Furthermore, the approach enables us to avoid strong assumptions. An example with real-world, empirical demand data is provided.     

The discrete-time preemptive repeat identical priority queue

Priority queueing systems come natural when customers with diversified delay requirements have to wait to get service. The customers that cannot tolerate but small delays get service priority over customers which are less delay-sensitive. In this contribution, we analyze a discrete-time two-class preemptive repeat identical priority queue with infinite buffer space and generally distributed service times. Newly arriving high-priority customers interrupt the on-going service of a low-priority customer. After all high-priority customers have left the system, the interrupted service of the low-priority customer has to be repeated completely. By means of a probability generating functions approach, we analyze the system content and the delay of both types of customers. Performance measures (such as means and variances) are calculated and the impact of the priority scheduling is discussed by means of some numerical examples.     

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.Research supported by the National Natural Science Foundation of China.