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

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

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

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

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

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

A MSFD complementary approach for the assessment of pressures, knowledge and data gaps in Southern European Seas : the PERSEUS experience

PERSEUS project aims to identify the most relevant pressures exerted on the ecosystems of the Southern European Seas (SES), highlighting knowledge and data gaps that endanger the achievement of SES Good Environmental Status (GES) as mandated by the Marine Strategy Framework Directive (MSFD). A complementary approach has been adopted, by a meta-analysis of existing literature on pressure/impact/knowledge gaps summarized in tables related to the MSFD descriptors, discriminating open waters from coastal areas. A comparative assessment of the Initial Assessments (IAs) for five SES countries has been also independently performed. The comparison between meta-analysis results and IAs shows similarities for coastal areas only. Major knowledge gaps have been detected for the biodiversity, marine food web, marine litter and underwater noise descriptors. The meta-analysis also allowed the identification of additional research themes targeting research topics that are requested to the achievement of GES. 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license.peer-reviewe

Waiting time analysis of multi-class queues with impatient customers

In this paper, we study three delay systems where different classes of impatient customers arrive according to independent Poisson processes. In the first system, a single server receives two classes of customers with general service time requirements, and follows a non-preemptive priority policy in serving them. Both classes of customers abandon the system when their exponentially distributed patience limits expire. The second system comprises parallel and identical servers providing the same type of service for both classes of impatient customers under the non-preemptive priority policy. We assume exponential service times and consider two cases depending on the time-to-abandon distribution being exponentially distributed or deterministic. In either case, we permit different reneging rates or patience limits for each class. Finally, we consider the first-come-first-served policy in single and multi-server settings. In all models, we obtain the Laplace transforms of the virtual waiting time for each class by exploiting the level-crossing method. This enables us to compute the steady-state system performance measures