When should service firms provide free experience service?

By providing a free experience service, a service firm can attract more uninformed customers. However, it could reversely effect the delay-sensitive, informed customers’ decision. In this paper, we study a priority queueing system with free experience services. We study the customer behavior in equilibrium after we derive the expected customer waiting time. We then construct the service firm’s revenue function and obtain an optimal strategy for the service firm. Our results suggest that when the market size of informed customers is relatively small, the firm should consider providing free experience services for uninformed customers. Conversely, if the demand rate of potential informed customers is quite high, the firm should ignore uninformed customers.     

Does inventory pooling improve customer service levels?

We study the risk pooling problem in a two-location inventory system, and analytically demonstrate that pooling improves the Type-I service levels at both locations. We also present an example showing that pooling may reduce the Type-II service levels at both locations.     

Heavy-traffic limits for many-server queues with service interruptions

We establish many-server heavy-traffic limits for G/M/n+M queueing models, allowing customer abandonment (the +M), subject to exogenous regenerative service interruptions. With unscaled service interruption times, we obtain a FWLLN for the queue-length process, where the limit is an ordinary differential equation in a two-state random environment. With asymptotically negligible service interruptions, we obtain a FCLT for the queue-length process, where the limit is characterized as the pathwise unique solution to a stochastic integral equation with jumps. When the arrivals are renewal and the interruption cycle time is exponential, the limit is a Markov process, being a jump-diffusion process in the QED regime and an O–U process driven by a Levy process in the ED regime (and for infinite-server queues). A stochastic-decomposition property of the steady-state distribution of the limit process in the ED regime (and for infinite-server queues) is obtained.     

Tandem queues with subexponential service times and finite buffers

We focus on tandem queues with subexponential service time distributions. We assume that number of customers in front of the first station is infinite and there is infinite room for finished customers after the last station but the size of the buffer between two consecutive stations is finite. Using (max, +) linear recursions, we investigate the tail asymptotics of transient response times and waiting times under both communication blocking and manufacturing blocking schemes. We also discuss under which conditions these results can be generalized to the tail asymptotics of stationary response times and waiting times.     

Queue lengths in the GIX/MR/∞ service system

Service systems with queueing often have both batch arrivals and batch services. This paper focuses on the number of busy servers and waiting customers in theGI ^X/M^R/ system. For the number of busy servers, we obtain a recursive relation for the partial binomial moments in terms of matrices and explicit expressions for the marginal binomial moments. Special cases are also discussed to provide a more heuristic understanding of the model.This research has been supported in part by the Natural Science and Engineering Council of Canada through Grant A5639.     

Factors shaping mathematics lecturers’ service teaching in different departments

In this article we focus on university lecturers’ approaches to the service teaching and factors that influence their approaches. We present data obtained from the interviews with 19 mathematics and three physics lecturers along with the observations of two mathematics lecturers’ calculus courses. The findings show that lecturers’ approaches to teaching the same topic vary across departments; that is, they consciously privilege different aspects of mathematics, set different questions on examinations and follow different textbooks while teaching in different departments. We discuss factors influencing lecturers’ decision of what (mathematics) to teach in different departments and offer educational implications for service mathematics teaching in terms of students’ mathematical needs and the role of mathematics for client students.     

Time-limited polling systems with batch arrivals and?phase-type service times

In this paper, we develop a general framework to analyze polling systems with either the autonomous-server or the time-limited service discipline. According to the autonomous-server discipline, the server continues servicing a queue for a certain period of time. According to the time-limited service discipline, the server continues servicing a queue for a certain period of time or until the queue becomes empty, whichever occurs first. We consider Poisson batch arrivals and phase-type service times. It is known that these disciplines do not satisfy the well-known branching property in polling systems. Therefore, hardly any exact results exist in the literature. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-lengths at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains.     

Mixed gated/exhaustive service in a polling model with priorities

In this paper we consider a single-server polling system with switch-over times. We introduce a new service discipline, mixed gated/exhaustive service, that can be used for queues with two types of customers: high and low priority customers. At the beginning of a visit of the server to such a queue, a gate is set behind all customers. High priority customers receive priority in the sense that they are always served before any low priority customers. But high priority customers have a second advantage over low priority customers. Low priority customers are served according to the gated service discipline, i.e. only customers standing in front of the gate are served during this visit. In contrast, high priority customers arriving during the visit period of the queue are allowed to pass the gate and all low priority customers before the gate. We study the cycle time distribution, the waiting time distributions for each customer type, the joint queue length distribution of all priority classes at all queues at polling epochs, and the steady-state marginal queue length distributions for each customer type. Through numerical examples we illustrate that the mixed gated/exhaustive service discipline can significantly decrease waiting times of high priority jobs. In many cases there is a minimal negative impact on the waiting times of low priority customers but, remarkably, it turns out that in polling systems with larger switch-over times there can be even a positive impact on the waiting times of low priority customers.     

Regression estimates of inputs to an M(t)/G/∞ service system

Three problems are solved: proof of convergence in distribution of a sequence {N^k(t)} of nonhomogeneous Poisson random variables to a nonhomogeneous Poisson random variable N(t); construction of a sequence of multiple linear regression models whose conditional expectations equal E(N^k(t)) (k = 1,2, …) aside from an additive constant; exploration of L₁ and L₂ criteria for estimating parameters of the regression models. Presentation of a numerical analysis of a case study involving a M(t)/M/∞ system of reproduction (arrivals) and mortality (services) within a biological population concludes the paper. Potential problems of interpreting parameter estimates obtained from linear programming implementations of the L₁ fitting criterion are analyzed.     

Large scale stochastic inventory routing problems with?split delivery and service level constraints

A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer??s delivery in each period can be split and satisfied by multiple vehicle routes if necessary. This paper considers SIRPSD under the multi-criteria of the total inventory and transportation costs, and the service levels of customers. The total inventory and transportation cost is considered as the objective of the problem to minimize, while the service levels of the warehouses and the customers are satisfied by some imposed constraints and can be adjusted according to practical requests. In order to tackle the SIRPSD with notorious computational complexity, we first propose an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We then develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model found by the approach is used to construct a near optimal solution of the SIRPSD. Randomly generated instances of the problem with up to 200 customers and 5 periods and about 400 thousands decision variables where half of them are integer are examined by numerical experiments. Our approach can obtain high quality near optimal solutions within a reasonable amount of computation time on an ordinary PC.     

Managerial insights from service industry models: a new scenario decomposition method

The service industry literature has recently assisted to the development of several new decision-support models. The new models have been often corroborated via scenario analysis. We introduce a new approach to obtain managerial insights in scenario analysis. The method is based on the decomposition of model results across sub-scenarios generated according to the high dimensional model representation theory. The new method allows analysts to quantify the effects of factors, their synergies and to identify the key drivers of scenario results. The method is applied to the scenario analysis of the workforce allocation model by Corominas et al. (Annals of Operations Research 128:217–233, 2004).     

Asymptotically optimal interruptible service policies for?scheduling jobs in a diffusion regime with?nondegenerate slowdown

A?parallel server system is considered, with I customer classes and many servers, operating in a heavy traffic diffusion regime where the queueing delay and service time are of the same order of magnitude. Denoting by $\widehat{X}^{n}$ and $\widehat{Q}^{n}$ , respectively, the diffusion scale deviation of the headcount process from the quantity corresponding to the underlying fluid model and the diffusion scale queue-length, we consider minimizing r.v.??s of the form $c^{n}_{X}=\int_{0}^{u}C(\widehat{X}^{n}(t))\,dt$ and $c^{n}_{Q}=\int_{0}^{u}C(\widehat{Q}^{n}(t))\,dt$ over policies that allow for service interruption. Here, C:? ^I ???₊ is continuous, and u>0. Denoting by ?? the so-called workload vector, it is assumed that $C^{*}(w):=\min\{C(q):q\in\mathbb{R}_{+}^{\mathbf{I}},\theta\cdot q=w\}$ is attained along a continuous curve as w varies in ?₊. We show that any weak limit point of $c^{n}_{X}$ stochastically dominates the r.v. $\int_{0}^{u}C^{*}(W(t))\,dt$ for a suitable reflected Brownian motion W and construct a sequence of policies that asymptotically achieve this lower bound. For $c^{n}_{Q}$ , an analogous result is proved when, in addition, C ^? is convex. The construction of the policies takes full advantage of the fact that in this regime the number of servers is of the same order as the typical queue-length.     

Efficient computational analysis of non-exhaustive service vacation queues: BMAP/R/1/N(∞) under gated-limited discipline

This paper analyzes the finite-buffer single server queue with vacation(s). It is assumed that the arrivals follow a batch Markovian arrival process (BMAP) and the server serves customers according to a non-exhaustive type gated-limited service discipline. It has been also considered that the service and vacation distributions possess rational Laplace-Stieltjes transformation (LST) as these types of distributions may approximate many other distributions appeared in queueing literature. Among several batch acceptance/rejection strategies, the partial batch acceptance strategy is discussed in this paper. The service limit L (1 ≤ L ≤ N) is considered to be fixed, where N is the buffer-capacity excluding the one in service. It is assumed that in each busy period the server continues to serve until either L customers out of those that were waiting at the start of the busy period are served or the queue empties, whichever occurs first. The queue-length distribution at vacation termination/service completion epochs is determined by solving a set of linear simultaneous equations. The successive substitution method is used in the steady-state equations embedded at vacation termination/service completion epochs. The distribution of the queue-length at an arbitrary epoch has been obtained using the supplementary variable technique. The queue-length distributions at pre-arrival and post-departure epoch are also obtained. The results of the corresponding infinite-buffer queueing model have been analyzed briefly and matched with the previous model. Net profit function per unit of time is derived and an optimal service limit and buffer-capacity are obtained from a maximal expected profit. Some numerical results are presented in tabular and graphical forms.     

The multiple server effect: Optimal allocation of servers to stations with different service‐time distributions in tandem queueing networks

Traditionally, studies on tandem queueing networks concentrate on systems with infinite buffers, exponential service times, and/or single servers where solutions are more tractable. Less research can be found on more general, less tractable systems. We examine multipleserver systems with finite buffers and nonexponential service times, studying the effects of coefficient of variation (cv) of the servicetime distribution on the throughput of these systems, where cv differs among stations.Starting with the single station, we examine the effects of cv and the number of servers at the station on the distribution of interdeparture times. This insight helps explain the differences in throughput seen in the single (fast) server vs. multiple (slow) server problem. These results, in turn, shed light on the server allocation problem when cv differs among stations. We present some observations, as well as the intuition behind them.