Analysis of the finite-source multiclass priority queue with an unreliable server and setup time

In this article, we study a queueing system serving multiple classes of customers. Each class has a finite-calling population. The customers are served according to the preemptive-resume priority policy. We assume general distributions for the service times. For each priority class, we derive the steady-state system size distributions at departure/arrival and arbitrary time epochs. We introduce the residual augmented process completion times conditioned on the number of customers in the system to obtain the system time distribution. We then extend the model by assuming that the server is subject to operation-independent failures upon which a repair process with random duration starts immediately. We also demonstrate how setup times, which may be required before resuming interrupted service or picking up a new customer, can be incorporated in the model

Spare parts provisioning for multiple k-out-of-n:G systems

In this paper, we consider a repair shop that fixes failed components from different k-out-of-n:G systems. We assume that each system consists of the same type of component; to increase availability, a certain number of components are stocked as spare parts. We permit a shared inventory serving all systems and/or reserved inventories for each system; we call this a hybrid model. Additionally, we consider two alternative dispatching rules for the repaired component. The destination for a repaired component can be chosen either on a first-come-first-served basis or by following a static priority rule. Our analysis gives the steady-state system size distribution of the two alternative models at the repair shop. We conduct numerical examples minimizing the spare parts held while subjecting the availability of each system to exceed a targeted value. Our findings show that unless the availabilities of systems are close, the HP policy is better than the HF policy

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

The dynamic nearest neighbor policy for the multi-vehicle pick-up and delivery problem

In this paper, a dynamic nearest neighbor (DNN) policy is proposed for operating a fleet of vehicles to serve customers, who place calls in a Euclidean service area according to a Poisson process. Each vehicle serves one customer at a time, who has a distinct origin and destination independently and uniformly distributed within the service area. The new DNN policy is a refined version of the nearest neighbor (NN) policy that is well known to perform sub-optimally when the frequency of customer requests is high. The DNN policy maintains geographically closest customer-to-vehicle assignments, due to its ability to divert/re-assign vehicles that may be already en-route to pick up other customers, when another vehicle becomes available or a new customer call arrives. Two other pertinent issues addressed include: the pro-active deployment of the vehicles by anticipating in which regions of the service area future calls are more likely to arise; and, imposition of limits to avoid prohibitively long customer wait times. The paper also presents accurate approximations for all the policies compared. Extensive simulations, some of which are included herein, clearly show the DNN policy to be tangibly superior to the first-comefirst-served (FCFS) and NN policies

On the use of phase-type distributions for inventory management with supply disruptions

Cataloged from PDF version of article.Maintaining the continuity of operations becomes increasingly important for systems that are subject to disruptions due to various reasons. In this paper, we study an inventory system operating under a (q, r) policy, where the supply can become inaccessible for random durations. The availability of the supply is modeled by assuming a single supplier that goes through ON and OFF periods of stochastic duration, both of which are modeled by phase-type distributions (PTD). We provide two alternative representations of the state transition probabilities of the system, one with integral and the other employing Kolmogorov differential equations. We then use an efficient formulation for the analytical model that gives the optimal policy parameters and the long-run average cost. An extensive numerical study is conducted, which shows that OFF time characteristics have a bigger impact on optimal policy parameters. The ON time characteristics are also important for critical goods if disasters can happen. Copyright (C) 2011 John Wiley & Sons, Ltd

Comparison of the effectiveness of chlorine, ozone, and photocatalytic disinfection in reducing the risk of antibiotic resistance pollution

Effectiveness of conventional chlorine and ozone disinfection on reduction of antibiotic resistance was compared with less commonly applied heterogeneous photocatalytic process. For this purpose plasmid DNA isolated from a multi-resistant Escherichia coli (E. coli) HB101 was treated in two different concentrations with the three oxidation processes. Oxidative damage on the plasmid DNA was analyzed with gel electrophoresis by comparing the extent of conformational changes in the DNA structure. The effectiveness of the applied oxidant in reducing the risk of resistance transfer was also evaluated by comparing the ability of treated plasmid DNA to transform competent cells. Chlorine did not affect plasmid DNA structure at the studied doses, while ozone and photocatalytic treatment resulted in conformational changes and the damage increased with increasing oxidant doses. Transformation experiments confirmed a similar trend. Chlorine did not affect the transformability and the cell counts of competent cells transformed with chlorine treated plasmid DNA were similar to those transformed by non-treated plasmid DNA in the control experiments

Coping with production time variability via dynamic lead-time quotation

In this paper, we propose two dynamic lead-time quotation policies in an M/GI/1 type make-to-stock queueing system serving lead-time sensitive customers with a single type of product. Incorporating non-exponential service times in an exact method for make-to-stock queues is usually deemed difficult. Our analysis of the proposed policies is exact and requires the numerical inversion of the Laplace transform of the sojourn time of an order to be placed. The first policy assures that the long-run probability of delivering the product within the quoted lead-time is the same for all backlogged customers. The second policy is a refinement of the first which improves the profitability if customers are oversensitive to even short delays in delivery. Numerical results show that both policies perform close to the optimal policy that was characterized only for exponential service times. The new insight gained is that the worsening impact of the production time variability, which is felt significantly in systems accepting all customers by quoting zero lead times, decreases when dynamic lead-time quotation policies are employed

A first passage time problem for spectrally positive Lévy processes and its application to a dynamic priority queue

We study a first passage time problem for a class of spectrally positive Lévy processes. By considering the special case where the Lévy process is a compound Poisson process with negative drift, we obtain the Laplace–Stieltjes transform of the steady-state waiting time distribution of low-priority customers in a two-class M/GI/1 queue operating under a dynamic non-preemptive priority discipline. This allows us to observe how the waiting time of customers is affected as the policy parameter varies

The impact of disruption characteristics on the performance of a server

In this paper, we study a queueing system serving N customers with an unreliable server subject to disruptions even when idle. Times between server interruptions, service times, and times between customer arrivals are assumed to follow exponential distributions. The main contribution of the paper is to use general distributions for the length of server interruption periods/down times. Our numerical analysis reveals the importance of incorporating the down time distribution into the model, since their impact on customer service levels could be counterintuitive. For instance, while higher down time variability increases the mean queue length, for other service levels, can prove to be improving system performance. We also show how the process completion time approach from the literature can be extended to analyze the queueing system if the unreliable server fails only when it is serving a customer

Scheduling policies for a repair shop problem

In this paper, we analyze a repair shop serving several fleets of machines that fail from time to time. To reduce downtime costs, a continuous-review spare machine inventory is kept for each fleet. A spare machine, if available on stock, is installed instantaneously in place of a broken machine. When a repaired machine is returned from the repair shop, it is placed in inventory for future use if the fleet has the required number of machines operating. Since the repair shop is shared by different fleets, choosing which type of broken machine to repair is crucial to minimize downtime and holding costs. The optimal policy of this problem is difficult to characterize, and, therefore, is only formulated as a Markov Decision Process to numerically compute the optimal cost and base-stock level for each spare machine inventory. As an alternative, we propose the dynamic Myopic(R) policy, which is easy to implement, yielding costs very close to the optimal. Most of the time it outperforms the static first-come-first-served, and preemptive-resume priority policies. Additionally, via our numerical study, we demonstrate that repair shop pooling is better than reserving a repair shop for each fleet