Strategies for a centralized single product multiclass M/G/1 make-to-stock queue

Make-to-stock queues are typically investigated in the M/M/1 settings. For centralized single-item systems with backlogs, the multilevel rationing (MR) policy is established as optimal and the strict priority (SP) policy is a practical compromise, balancing cost and ease of implementation. However, the optimal policy is unknown when service time is general, i.e., for M/G/1 queues. Dynamic programming, the tool commonly used to investigate the MR policy in make-to-stock queues, is less practical when service time is general. In this paper we focus on customer composition: the proportion of customers of each class to the total number of customers in the queue. We do so because the number of customers in M/G/1 queues is invariant for any nonidling and nonanticipating policy. To characterize customer composition, we consider a series of two-priority M/G/1 queues where the first service time in each busy period is different from standard service times, i.e., this first service time is exceptional. We characterize the required exceptional first service times and the exact solution of such queues. From our results, we derive the optimal cost and control for the MR and SP policies for M/G/1 make-to-stock queues

Pricing and admission control for shared computer services using the token bucket mechanism

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, 2003.Includes bibliographical references (p. 196-199).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.This dissertation presents and analyzes token-bucket pricing schemes for shared resources. This research is motivated by the computer services industry, where services are provided mostly on a dedicated basis. However, leading computer companies such as HP and IBM forecast that external service providers will share resources between customers, in order to realize economies of scale. Two of the challenges faced by providers and consumers of shared services are admission control and pricing. In order to allow sellers to guarantee service levels, we recommend that pricing schemes for shared resources include admission controls. The implementation of such schemes requires understanding of buyers' and sellers' actions and a characterization of the admission control. This dissertation reviews the computer services supply-chain and proposes a five-step procedure for analyzing the pricing of shared services. Then it extends the usage of token-bucket and token-bucket-with-rate-control admission controls to pricing schemes. We show that for the token-bucket (token-bucket-with-rate-control) mechanism the bucket level behaves as a two- (one-) sided regulated random walk. Thus, the performance analysis (loss sales or backlog) is identical to the analysis of threshold crossing probabilities of regulated random walks. This dissertation's main contribution is an upper bound on the probability of a two-sided regulated random walk being on its "rare" boundary. Using the bounds developed, we solve constrained or relaxed versions of the buyer's problem. For the token-bucket-with-rate-control pricing scheme and exponential demand the buyer's problem can be solved in closed form.(cont.) Moreover, numerical experiments show that the approximate solutions for the normal demand case are within 1% of optimal. Similar results hold for the token-bucket mechanism. Finally, we characterize the output stream of these admission controls (the jumps of one- or two-sided regulated random walks). We use a Brownian motion approximation for the bucket level process, but still consider the actual demand and arrival processes. Moreover, we enhance the performance of this approach by relating fill rates with the percentage of periods with losses. Numerical results show that in both mechanisms, when demand is exponential or normal, the approximated first two moments of the output stream are, typically, within the 99% confidence intervals.by Opher Baron.Ph.D

M/M/c queue with two priority classes

This paper provides the first exact analysis of a preemptive M/M/c queue with two priority classes having different service rates. To perform our analysis, we introduce a new technique to reduce the two-dimensionally infinite Markov chain (MC), representing the two class state space, into a one-dimensionally infinite MC, from which the generating function (GF) of the number of low-priority jobs can be derived in closed form. (The high-priority jobs form a simple M/M/c system and are thus easy to solve.) We demonstrate our methodology for the c = 1, 2 cases; when c > 2, the closed-form expression of the GF becomes cumbersome. We thus develop an exact algorithm to calculate the moments of the number of low-priority jobs for any c ≥ 2. Numerical examples demonstrate the accuracy of our algorithm and generate insights on (i) the relative effect of improving the service rate of either priority class on the mean sojourn time of low-priority jobs; (ii) the performance of a system having many slow servers compared with one having fewer fast servers; and (iii) the validity of the square root staffing rule in maintaining a fixed service level for the low-priority class. Finally, we demonstrate the potential of our methodology to solve other problems using the M/M/c queue with two priority classes, where the high-priority class is completely impatient.Accepted versio

Bargaining in competing supply chains with uncertainty

Substantial literature has been devoted to supply chain coordination. The majority of this literature ignores competition between supply chains. Moreover, a significant part of this literature focuses on coordination that induce the supply chain members to follow strategies that produce the equilibria chosen by a vertically integrated supply chain. This paper investigates the equilibrium behavior of two competing supply chains in the presence of demand uncertainty. We consider joint pricing and quantity decisions and competition under three possible supply chain strategies: Vertical Integration (VI), Manufacturer's Stackelberg (MS), and Bargaining on the Wholesale price (BW([alpha]), [alpha] is the bargaining parameter) over a single or infinitely many periods. We show that, in contrast to earlier literature, using VIVI (VI in both chains) is the unique Nash Equilibrium over one period decision, while using MSMS or BW([alpha])BW([alpha]) may be Nash Equilibrium over infinitely many periods.Competing supply chain Uncertain demand Bargaining Channel coordination

Now Playing: DVD Purchasing for a Multilocation Rental Firm

This paper studies the problem of purchasing and allocating copies of movies to multiple stores of a movie rental chain. A unique characteristic of this problem is the return process of rented movies. We formulate this problem for new movies as a newsvendor-like problem with multiple rental opportunities for each copy. We provide demand and return forecasts at the store-day level based on comparable movies. We estimate the parameters of various demand and return models using an iterative maximum-likelihood estimation and Bayesian estimation via Markov chain Monte Carlo simulation. Test results on data from a large movie rental firm reveal systematic underbuying of movies purchased through revenue-sharing contracts and overbuying of movies purchased through standard (nonrevenue-sharing) ones. For the movies considered, our model estimates an increase in the average profit per title for new movies by 15.5% and 2.5% for revenue sharing and standard titles, respectively. We discuss the implications of revenue sharing on the profitability of the rental firm.service operations, supply chain management, inventory theory and control

Facility Location with Stochastic Demand and Constraints on Waiting Time

We analyze the problem of optimal location of a set of facilities in the presence of stochastic demand and congestion. Customers travel to the closest facility to obtain service; the problem is to determine the number, locations, and capacity of the facilities. Under rather general assumptions (spatially distributed continuous demand, general arrival and service processes, and nonlinear location and capacity costs) we show that the problem can be decomposed, and construct an efficient optimization algorithm. The analysis yields several insights, including the importance of equitable facility configurations (EFCs), the behavior of optimal and near-optimal capacities, and robust class of solutions that can be constructed for this problem.facility location, stochastic demand, queueing, service level

Using strategic idleness to improve customer service experience in service networks

The most common measure of waiting time is the overall expected waiting time for service. However, in service networks the perception of waiting may also depend on how it is distributed among different stations. Therefore, reducing the probability of a long wait at any station may be important in improving customers' perception of service quality. In a single-station queue it is known that the policy that minimizes the waiting time and the probability of long waits is nonidling. However, this is not necessarily the case for queueing networks with several stations. We present a family of threshold-based policies (TBPs) that strategically idle some stations. We demonstrate the advantage of strategically idling by applying TBP in a network with two single-server queues in tandem. We provide closed form results for the special case where the first station has infinite capacity and develop efficient algorithms when this is not the case. We compare TBPs with the nonidling and Kanban policies, and we discuss when a TBP is advantageous. Using simulation, we demonstrate that the analytical insights for the two-station case hold for a three-station serial queue as well.Accepted versio