Strategic revenue management of preemptive versus non-preemptive queues

Consider a two-class unobservable priority queue, with Poisson arrivals, generally distributed service, and strategic customers. Customers are charged a fee when joining the premium class. We analyze the maximum revenue achievable under the non-preemptive (NP) and preemptive-resume (PR) policies, and show that a provider is always better off implementing the PR policy. Further, the maximum revenue under PR is sometimes achieved when only a fraction of the customers join the premium class.     

Threshold-based interventions to optimize performance in preemptive priority queues

This paper studies a single-server priority queueing model in which preemptions are allowed during the early stages of service. Once enough service effort has been rendered, however, further preemptions are blocked. The threshold where the change occurs is either a proportion of the service requirement, or time-based. The Laplace–Stieltjes transform and mean of each class sojourn time are derived for a model which employs this hybrid preemption policy. Both preemptive resume and preemptive repeat service disciplines are considered. Numerical examples show that it is frequently the case that a good combination of preemptible and nonpreemptible service performs better than both the standard preemptive and nonpreemptive queues. In a number of these cases, the thresholds that optimize performance measures such as overall average sojourn time are determined. This revised version was published online in June 2006 with corrections to the Cover Date.     

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.     

The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands

By showing that there is an upper bound for the price of anarchyρ(Γ) for a non-atomic congestion game Γ with only separable cost maps and fixed demands, Roughgarden and Tardos show that the cost of forgoing centralized control is mild. This letter shows that there is an upper bound for ρ(Γ) in Γ for fixed demands with symmetric cost maps. It also shows that there is a weaker bound for ρ(Γ) in Γ with elastic demands.     

Revenue-sharing versus wholesale price mechanisms under different channel power structures

We consider a supply chain channel with two manufacturers and one retailer. Each manufacturer can choose either a wholesale price contract or a revenue-sharing contract with the retailer. We discuss and compare the results of two different types of contracts under different channel power structures, to check whether it is beneficial for manufacturers to use revenue-sharing contracts under different scenarios. Then we consider a supply chain channel with one manufacturer and two retailers. Each retailer can choose either a wholesale price contract or a revenue-sharing contract with the manufacturer. We analyze the likely outcomes under different scenarios to discover whether it is beneficial to use revenue-sharing contracts.     

A preemptive repeat priority queue with resampling: Performance analysis

In this paper, we analyze a discrete-time preemptive repeat priority queue with resampling. High-priority packets have preemptive repeat priority, and interrupted low-priority packets are subjected to independent retransmission attempts. Both classes contain packets with generally distributed transmission times. We show that the use of generating functions is beneficial for analyzing the system contents and packet delay of both classes. The influence of the priority scheduling on the performance measures is illustrated by some numerical examples. This work has been supported by the Interuniversity Attraction Poles Programme–Belgian Science Policy.     

Random queues and risk averse users

We analyze Nash equilibrium in time of use of a congested facility. Users are risk averse with general concave utility. Queues are subject to varying degrees of random sorting, ranging from strict queue priority to a completely random queue. We define the key “no residual queue” property, which holds when there is no queue at the time the last user arrives at the queue, and prove that this property holds in equilibrium under all queueing regimes considered. The no residual queue property leads to simple results concerning the equilibrium utility of users and the timing of the queue.     

Equilibrium analysis in batch-arrival queues with complementary services

This paper studies a batch-arrival queue with two complementary services. The two services are complementary and any customer has no benefit from obtaining just one of them. To the best of the authors’ knowledge, there are no works contributed to the batch-arrival queues on analysis of the equilibrium behaviors in queueing systems by now. The properties of batch-arrival queues, which is more practical and universal in reality, induce different Nash equilibria under competition or monopoly compared with the single-arrival queues. We observe the joint effect of batch joining rate and cost structure on the behavior of customers and graphically interpret the equilibrium solutions under competition. Moreover, we discuss the model under three types of price structures and give comparisons from customer and server points.     

A dynamic model for advertising and pricing competition between national and store brands

We study the relationship between the pricing and advertising decisions in a channel where a national brand is competing with a private label. We consider a differential game that incorporates the carryover effects of brand advertising over time for both the manufacturer and the retailer and we account for the complementary and competitive roles of advertising. Analysis of the obtained equilibrium Markov strategies shows that the relationship between advertising and pricing decisions in the channel depends mainly on the nature of the advertising effects. In particular, the manufacturer reacts to higher competitive retailer’s advertising levels by offering price concessions and limiting his advertising expenditures. The retailer’s optimal reaction to competitive advertising effects in the channel depends on two factors: (1) the price competition level between the store and the national brands and (2) the strength of the competitive advertising effects. For example, in case of intense price competition between the two brands combined with a strong manufacturer’s competitive advertising effect, the retailer should lower both the store and the national brands’ prices as a reaction to higher manufacturer’s advertising levels. For the retailer, the main advantage from boosting his competitive advertising investments seems to be driven by increased revenues from the private label. The retailer should however limit his investments in advertising if the latter generates considerable competitive effects on the national brand’s sales.     

Recursive calculation of moments in priority queues

We reconsider the discrete-time priority queue with two classes. The server serves high-priority customers as long as there are such customers, and only turns to the low-priority customers when there are no high-priority customers. Relying on a multivariate recursive extension of Faà di Bruno's formula, we find recursive equations to calculate the moments of the queue lengths. This allows for calculation of many more moments in much shorter time than conventionally possible.     

Linear programming based algorithms for preemptive and non-preemptive RCPSP

In this paper, the RCPSP (resource constrained project scheduling problem) is solved using a linear programming model. Each activity may or may not be preemptive. Each variable is associated to a subset of independent activities (antichains). The properties of the model are first investigated. In particular, conditions are given that allow a solution of the linear program to be a feasible schedule. From these properties, an algorithm based on neighbourhood search is derived. One neighbour solution is obtained through one Simplex pivoting, if this pivoting preserves feasibility. Methods to get out of local minima are provided. The solving methods are tested on the PSPLIB instances in a preemptive setting and prove efficient. They are used when preemption is forbidden with less success, and this difference is discussed.     

Pricing policies for substitutable products in a supply chain with Internet and traditional channels

This study considers pricing policies in a supply chain with one manufacturer, who sells a product to an independent retailer and directly to consumers through an Internet channel. In addition to the manufacturer’s product, the retailer sells a substitute product produced by another manufacturer. Given the wholesale prices of the two substitute products, the manufacturer decides the retail price of the Internet channel, and the retailer decides the retail prices of the two substitute products. Both the manufacturer and the retailer choose their own decision variables to maximize their respective profits. This work formulates the price competition, using the settings of Nash and Stackelberg games, and derives the corresponding existence and uniqueness conditions for equilibrium solutions. A sensitivity analysis of an equilibrium solution is then conducted for the model parameters, and the profits are compared for two game settings. The findings show that improving brand loyalty is profitable for both of the manufacturer and retailer, and that an increased service value may alleviate the threat of the Internet channel for the retailer and increase the manufacturer’s profit. The study also derives some conditions under which the manufacturer and the retailer mutually prefer the Stackelberg game. Based on these results, this study proposes an appropriate cooperation strategy for the manufacturer and retailer.     

Deregulation and welfare in airline markets: An analysis of frequency equilibria

This paper models airline competition as a two-stage game in frequency and prices, allowing for asymmetric frequency equilibria. The approach follows the spatial multiproduct oligopoly literature. The dynamic structure gives airlines an incentive to choose asymmetric frequency equilibria such that price competition is reduced. This feature is most pronounced in the case of inelastic demand, for which a maximum differentiation result is derived. We apply the model in a simulation study of airline deregulation of the Amsterdam—Maastricht market in The Netherlands, calculating welfare effects for various types of post-deregulation entry.     

A genetic algorithm for the preemptive and non-preemptive multi-mode resource-constrained project scheduling problem

In this paper we present a genetic algorithm for the multi-mode resource-constrained project scheduling problem (MRCPSP), in which multiple execution modes are available for each of the activities of the project. We also introduce the preemptive extension of the problem which allows activity splitting (P-MRCPSP). To solve the problem, we apply a bi-population genetic algorithm, which makes use of two separate populations and extend the serial schedule generation scheme by introducing a mode improvement procedure. We evaluate the impact of preemption on the quality of the schedule and present detailed comparative computational results for the MRCPSP, which reveal that our procedure is amongst the most competitive algorithms.     

The price of anarchy in an exponential multi-server

We consider two criteria for routing selection in a multi-server service station: the equilibrium and social optimization. The ratio between the average mean waiting times in these two routings is called the price of anarchy (PoA). We show that the worst-case PoA is precisely the number of servers.     

Conditions of reverse bullwhip effect in pricing for price-sensitive demand functions

Supply chain mechanisms that exacerbate price variation needs special attention, since price variation is one of the root causes of the bullwhip effect. In this study, we investigate conditions that create an amplification of price variation moving from the upstream suppliers to the downstream customers in a supply chain, which is referred as the “reverse bullwhip effect in pricing” (RBP). Considering initially a single-stage supply chain in which a retailer faces a random and price-sensitive demand, we derive conditions on a general demand function for which the retail price variation is higher than that of the wholesale price. The investigation is extended to a multi-stage supply chain in which the price at each stage is determined by a game theoretical framework. We illustrate the use of the conditions in identifying commonly used demand functions that induce RBP analytically and by means of several numerical examples.     

Reverse bullwhip effect in pricing

Price variability is one of the major causes of the bullwhip effect. This paper analyzes the impact of procurement price variability in the upstream of a supply chain on the downstream retail prices. Procurement prices may fluctuate over time, for example, when the supply chain players deploy auction type procurement mechanisms, or if the prices are dictated in market exchanges. A game theory framework is used here to model a serial supply chain. Sequential price game scenarios are investigated to show that there is an increase in retail price variability and an amplified reverse bullwhip effect on prices (RBP) under certain demand conditions.     

Analysis of nonpreemptive priority queues with multiple servers and two priority classes

In this paper, we model a priority multiserver queueing system with two priority classes. A high priority customer has nonpreemptive priority over low priority customers. The approaches for solving the problem are the state-reduction based variant of Kao, the modified boundary algorithm of Latouche, the logarithmic reduction algorithm of Latouche and Ramaswami, and the power-series method of Blanc. The objectives of this paper are to present a power-series implementation for the priority queue and to evaluate the relative efficiencies of alternative procedures to compute various performance characteristics. In the paper, we find that at times the logarithmic reduction algorithm may not perform as well as expected and the power-series approach can occasionally pose numerical difficulties.     

Mixing of non-preemptive and preemptive repeat priority disciplines

A single server dispenses service to m priority classes. The arrival process of the ith class, i = 1, 2,…,m, is homogeneous Poisson. 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 j ? i > d (where d is a predetermined non-negative integer), and non-preemptive priority otherwise. An interrupted service is resumed when the system contains no costomers with higher priority, preemptive and non-preemptive. Within each priority class the FIFO rule is obeyed.The preemptive regimes analyzed are repeat with and without resampling. For a k-customer, k = 1, 2,…,n, steady-state Laplace-Stieltjes transforms, and expectations of the waiting time and the time in the system are calculated.