Customer Classes Research Articles

Performance of Stochastic Inventory System with a Fresh Item, Returned Item, Refurbished Item, and Multi-Class Customers

This paper deals with an integrated and interconnected stochastic queuing-inventory system with a fresh item, a returned item, and a refurbished item. This system provides a multi-type service facility to an arriving multi-class customer through a dedicated channel. It sells fresh and refurbished items, buys used items from customers, refurbishes the used items for resale, and provides a repair service for defective items. The assumption of purchasing a used item from the customer and allowing them to buy a fresh item is a new idea in stochastic queuing-inventory modeling. To do so, this system has four parallel queues to receive four classes of customers and five dedicated servers to provide a multi-type service facility. Customers are classified according to the type of service they require. Each class of arrival follows an independent Poisson process. The service time of each dedicated server is assumed to be exponentially distributed and independent. This system assumes an instantaneous ordering policy for the replenishment of a fresh item. In the long run of this considered system, the joint probability distribution of the seven-dimensional stochastic process, significant system performance measures, and the optimum total cost are to be derived using the Neuts matrix geometric technique. The main objective of the system was to increase the occurrence of all kinds of customers by providing a multi-type service facility in one place. Buying a used item is unavoidable in an emerging society because it helps form a green society. Furthermore, the numerical result shows that the assumption of a system that allows a customer to sell their used item and purchase a new item will increase the number of customers approaching the system.

N , n -Preemptive-Priority M/G/1 Queues with Finite and Infinite Buffers

In this paper, we analyze an M/G/1 priority queueing model with finite and infinite buffers under the N , n -preemptive priority discipline, under which preemption decisions are made based on the number of high-priority customers. This priority queueing model can be used for the performance analysis of communication systems accommodating delay- and loss-sensitive packets simultaneously. To analyze the proposed model, we extend the method of delay cycle analysis and develop a queue length version of it for finite-buffer queues. Throughout our analysis, we demonstrate that by the proposed method the analysis of the complex priority queueing model can be reduced to that of simple delay cycles, so two different preemption modes of the queueing model can be dealt with in a unified way. The numerical study reveals that adjusting the decision variables N and n allows us to fine-tune system performance for different classes of customers, and N operates as a primary control variable, regardless of the preemption mode and service-time distributions.

Balanced routing with partial information in a distributed parallel many-server queueing system

We consider a queueing system that is comprised of multiple stations serving a single class of customers. Each station consists of many statistically identical servers, and has its own dedicated queue. In this paper, we propose a family of generalized load-balancing routing policies parameterized by vectors c and d with ξ-choice (abbreviated as LB(ξ,c,d)), that are suitable for dynamic routing with partial state information. Under the proposed policy, upon an arrival, a subset of ξ stations will be randomly collected, with their state information being retrieved, where ξ is a positive integer-valued random variable satisfying P{ξ≥2}>0; then, this new customer will be routed to: (i) the station with minimum expected delay modified by c when all the collected stations are fully occupied; or otherwise (ii) the station with maximum idleness ratio modified by d among the collected stations with idle servers. The parameters c and d are employed to control the relative expected delay and utilization levels across stations. Using asymptotic analysis, we derive diffusion limits of queue-length processes as well as their stationary distributions under the LB(ξ,c,d) policy in the Halfin–Whitt regime. Based on these stationary diffusion limit results, we develop a solution procedure to determine policy parameters under different optimization criteria. Finally, we provide numerical experiments to validate the accuracy of our diffusion approximation, and compare the performances under the LB(ξ,c,d) policies with other routing policies.

A Multi-Type Queueing Inventory System—A Model for Selection and Allocation of Spectra

The model discussed in this paper provides an efficient mechanism for the selection and allocation of available limited spectra for transmission of heterogeneous data in a network. The data packets (customers), belonging to different classes, arrive according to a batch marked the Markovian arrival process (BMMAP). The inventory considered is of multi-type (different types of channels becoming available) and are generated according to a marked Markovian arrival process (MMAP). The number of distinct types of inventory and that of the customers are the same. Arriving customers are allowed to wait in finite buffers of each category which are reserved for distinct classes of customers except for the most general class, which is provided with an infinite waiting space. The number of servers also equals the number of distinct types of inventory. When items of a particular type arrive in the inventory, the service starts, providing the buffer of customers of the corresponding class is non-empty. The service can be viewed as a selection process with Coxian distributed service times. The system is analyzed using the matrix analytic method and performance measures are obtained. The model is illustrated with suitable numerical examples.

On System-Wide Safety Staffing of Large-Scale Parallel Server Networks

Large-scale stochastic networks are widely used for a variety of systems including telecommunications, patient flows, service and data centers, and so on. Because of their complexity, ensuring the stability of these networks by allocating the required resources needed by each customer class is quite challenging. When there are sufficient resources to serve each customer class, the existence of a policy that stabilizes the system is trivial. One can decouple the network and assign the required resources to each customer class. Conversely, one can anticipate that, when each class is resourceless, it is impossible to stabilize the system independent of the policy used. However, previous analyses did not tackle this question. In this work, we assume that some classes have excess resources, whereas others are deficient. We provide a full characterization of the stability of these networks by identifying a parameter that describes the overall excess or lack of resources in the network.

Algorithms for Queueing Systems with Reneging and Priorities Modeled as Quasi-Birth-Death Processes

We consider a Markovian multiserver queueing system with two customer classes, preemptive priorities, and reneging. We formulate this system as an infinite level-dependent quasi-birth-death process (LDQBD). We introduce an algorithm that endogenously truncates the level and calculates lower and upper bounds on stationary probabilities of this LDQBD such that the gap between the bounds can be any desired amount. Our algorithm can be applied to any LDQBD for which the rate matrices become elementwise nonincreasing above some level. This appears to be the first algorithm that provides bounds on stationary probabilities for an infinite-level LDQBD. To obtain these bounds, the algorithm first obtains lower and upper bounds on the rate matrices of the LDQBD using a novel method, which can be applied to any LDQBD. We then extend this algorithm to approximate performance measures of the system of interest and calculate exact lower and upper bounds for those that can be expressed as probabilities, such as the probability that an incoming low-priority customer will wait. We generate a wide range of instances with up to 100 servers and compare the solution times and accuracy of our algorithm with two existing algorithms. These numerical experiments indicate that our algorithm is faster than the other two algorithms for a given accuracy requirement. We investigate the impact of changing service rates on the proportion of low-priority customers served and their wait time, and we demonstrate how ignoring one of these measures can possibly mislead decision makers. Summary of Contribution: We contribute to operations research by modeling a practically important queueing system and developing an algorithm to accurately compute performance measures for that system. We also contribute to computer science by providing error and complexity analysis for the algorithm to solve a broad class of two-dimensional Markov chains with infinite state space.

Admission Control Game with Capacity Borrowing

We study a decentralized admission control problem with capacity borrowing. In this problem, the admission decision is made by each server who is assigned dedicated capacity. However, a server can borrow capacity from other servers if his dedicated capacity is exhausted. The borrower compensates the lender by a payment equal to the “borrowing cost.” Hence, the servers share their capacities via borrowing, but they also compete against each other for their pooled capacities. We formulate this problem as a stochastic dynamic game and characterize the equilibrium strategic admission behavior of servers. We show that the critical factors that affect the equilibrium behavior and the system revenue are the magnitude of the borrowing cost, the arrival rate of customers and the revenue difference between different classes of customers. We have identified conditions under which servers maximizing their own payoffs end up making decisions that benefit the system. Our study highlights the important roles that the borrowing cost plays in shaping servers’ behavior in service systems and provides concrete guidance for practitioners to design a decentralized admission control system.

Instability of SRPT, SERPT and SJF multiclass queueing networks

We provide two examples of strictly subcritical multiclass queueing networks which are unstable under the shortest remaining processing time (SRPT) service protocol. Both of them are reentrant lines with two servers and eight customer classes. The customer service times in our first system are deterministic, yielding an example of an unstable shortest remaining expected processing time (SERPT) network. In the second one, the service times in one customer class are randomized. Both our examples show also system instability under the shortest job first (SJF) discipline. A simulation study of robustness of our results with respect to changes in the customer interarrival and service times is also provided. Our results indicate that size-based service policies may not use the available resources efficiently in a multiserver network setting and in fact cause instability effects. This is in sharp contrast with their satisfactory performance for single-server queues.

Reliability and Optimization Measures of Retrial Queue with Different Classes of Customers under a Working Vacation Schedule

A working vacation queueing model is described in this work, with three different classes of customers: regular, priority, and disaster. The regular server serves all arriving customers, whereas the optional reservice is only provided to those who request it. The Bernoulli working vacation (BWV) schedule is considered. In WV time, the server serves at a slower rate. The generating functions (GF) technique is used to determine the system capacity of various server states. Different system performances, reliability indices, and cost optimization values are numerically shown. For the current COVID‐19 pandemic situation, the motivation for this approach is presented in a telephonic communication system.

When to Triage in Service Systems with Hidden Customer Class Identities?

In service systems with heterogeneous customers, prioritization with respect to the relative importance of customers is known to improve certain performance measures. However, in many applications, information necessary to determine the importance level of a customer may not be available immediately but can be revealed only through some preliminary investigation, which is sometimes called triage. This triage process is typically error‐prone and may take substantial amount of time, and hence, it is not always clear if and when it should be implemented for purposes of priority assignment. To provide insights into this question, we study a stylized queueing model with a single server and two types of customers with hidden type identities, which differ in their rates of service and waiting costs. By means of a Markov decision formulation, we first show that the optimal dynamic policy on triage is characterized by a switching curve. The comparison of two state‐independent policies (no‐triage and triage‐all) shows that the information from triage is more beneficial when the traffic intensity is neither too low nor too high. Our numerical results show that the system manager should consider implementing a state‐dependent triage policy when the probability of classifying a customer into the important class and the mean triage time are of moderate size, when the difference between the importance levels of the two classes of customers is large, and/or when the traffic intensity is high.

Identification of customers’ purchasing behaviour profiles in the context of corporate social responsibility

Purpose: The aim of the article is to identify customers' purchasing behaviour profiles on the basis of characterizing the process of making a decision to purchase a product from food industry companies’ indicators (observable variables) in the context of corporate social responsibility (CSR). Design/methodology/approach: The data for the research were collected from a survey concerning a group of 801 customers from the Świętokrzyskie Voivodeship. The resources were pre-explored and pre-processed to enable further studies. In order to obtain customers profiles, the latent class analysis (LCA) method was used. It enables identification of homogeneous groups (latent classes) of customers based on selected indicators. Findings: The impact on customers’ purchasing behaviour of 15 CSR activities undertaken by enterprises from several different groups (in relation to: environment, society, employees, contractors, and customers) was examined. Six profiles of customer purchasing behaviour were identified. They were labelled and subjected to descriptive characteristics. Research limitations/implications: The results point out the need to continue the research based on a broader countrywide data set. Practical implications: The research findings can contribute to improving the effectiveness of food industry companies in the range of CSR activities. Due to this, these companies will be able to take more effective steps to retain existing customers and acquire new ones. Social implications: Taking corporate social responsibility actions contributes to solve social and environmental problems. It can also affect the quality of life in a society. Nowadays, it is an important and developmental research area. Originality/value: The conducted study showed that latent class analysis is proper tool for analysing the qualitative data obtained in the questionnaire surveys. The work provides a vital information on the impact of corporate social responsibility activities by food industry companies on customers' purchasing behaviour. Keywords: corporate social responsibility, customer profiles, purchasing behaviour, food industry, latent class analysis. Category of the paper: Research paper.

Demographic Factors, Level of Awareness and Banking Service as Intervening Factor: A Study of SBI in Cuttack City, Odisha

The Indian banking industry has transformed into one of the promising industries that offer services through multiple channels with the help of information systems and technology. Banking is essentially a high contact service industry and there is close communication between service providers to customers. Customer awareness and satisfaction about financial products and services are very crucial for the success of any Bank. The current banking technology allows the customer to buy products or consumer services using their bank account and other services from any place. The study aims to trace the usage behaviour of various services by a different class of customers and their satisfaction towards the services rendered by Banks. The present study is completely Descriptive. Both primary, as well as secondary data, were used for the study. State bank of India (SBI) was selected based on the ground of concentration of public sector Banks in that area. It is found that all the demographic variables are strongly related to the level of awareness towards banking products and services.

Queues with Redundancy: Is Waiting in Multiple Lines Fair?

Problem definition: We study service systems where some (so-called “redundant”) customers join multiple queues simultaneously, enabling them to receive service in any one of the queues, while other customers join a single queue. Academic/practical relevance: The improvement in overall system performance due to redundant customers has been established in prior work. We address the question of fairness—whether the benefit experienced by redundant customers adversely affects others who can only join a single line. This question is particularly relevant to organ transplantation, as critics have contended that multiple listing provides unfair access to organs for patients based on wealth. Methodology: We analyze two queues serving two classes of customers; the redundant class joins both queues, whereas the nonredundant class joins a single queue randomly. We compare this system against a benchmark wherein the redundant class resorts to joining the shortest queue (JSQ) if multiple queue joining were not allowed, capturing the most likely case if multilisting was prohibited: Affluent patients could still afford to list in the region with the shorter wait list. Results: We prove that when the arrival rate of nonredundant customers is balanced across both queues, they actually benefit under redundancy of the other class—that is, redundancy is fair. We also establish that redundancy may be unfair under some circumstances: Nonredundant customers are worse off if their arrival rate is strongly skewed toward one of the queues. We illustrate how these findings apply in the organ-transplantation setting through a numerical study using publicly available data. Managerial implications: Our analysis helps identify when, and by how much, multiple listing may be unfair and, as such, could be a useful tool for policy makers who may be concerned with trying to ensure equitable access to resources, such as organs, across patients with differing wealth levels.

Optimal Scheduling of Proactive Service with Customer Deterioration and Improvement

Service systems are typically limited resource environments where scarce capacity is reserved for the most urgent customers. However, there has been a growing interest in the use of proactive service when a less urgent customer may become urgent while waiting. On one hand, providing service for customers when they are less urgent could mean that fewer resources are needed to fulfill their service requirement. On the other hand, using limited capacity for customers who may never need the service in the future takes the capacity away from other more urgent customers who need it now. To understand this tension, we propose a multiserver queueing model with two customer classes: moderate and urgent. We allow customers to transition classes while waiting. In this setting, we characterize how moderate and urgent customers should be prioritized for service when proactive service for moderate customers is an option. We identify an index, the modified [Formula: see text]-index, which plays an important role in determining the optimal scheduling policy. This index lends itself to an intuitive interpretation of how to balance holding costs, service times, abandonments, and transitions between customer classes. This paper was accepted by David Simchi-Levi, stochastic models and simulation.

Fluid Limits for Multiclass Many-Server Queues with General Reneging Distributions and Head-of-the-Line Scheduling

We describe a fluid model with time-varying input that approximates a multiclass many-server queue with general reneging distribution and multiple customer classes (specifically, the multiclass G/GI/N+GI queue). The system dynamics depend on the policy, which is a rule for determining when to serve a given customer class. The class of admissible control policies are those that are head-of-the-line (HL) and nonanticipating. For a sequence of many-server queues operating under admissible HL control policies and satisfying some mild asymptotic conditions, we establish a tightness result for the sequence of fluid scaled queue state descriptors and associated processes and show that limit points of such sequences are fluid model solutions almost surely. The tightness result together with the characterization of distributional limit points as fluid model solutions almost surely provides a foundation for the analysis of particular HL control policies of interest. We leverage these results to analyze a set of admissible HL control policies that we introduce, called weighted random buffer selection (WRBS), and an associated WRBS fluid model that allows multiple classes to be partially served in the fluid limit (which is in contrast to previously analyzed static priority policies).

On first-come, first-served queues with three classes of impatient customers

On first-come, first-served queues with three classes of impatient customers

Steady State Analysis of Impulse Customers and Cancellation Policy in Queueing-Inventory System

This article discusses the queueing-inventory model with a cancellation policy and two classes of customers. The two classes of customers are named ordinary and impulse customers. A customer who does not plan to buy the product when entering the system is called an impulse customer. Suppose the customer enters into the system to buy the product with a plan is called ordinary customer. The system consists of a pool of finite waiting areas of size N and maximum S items in the inventory. The ordinary customer can move to the pooled place if they find that the inventory is empty under the Bernoulli schedule. In such a situation, impulse customers are not allowed to enter into the pooled place. Additionally, the pooled customers buy the product whenever they find positive inventory. If the inventory level falls to s, the replenishment of Q items is to be replaced immediately under the (s, Q) ordering principle. Both arrival streams occur according to the independent Markovian arrival process (MAP), and lead time follows an exponential distribution. In addition, the system allows the cancellation of the purchased item only when there exist fewer than S items in the inventory. Here, the time between two successive cancellations of the purchased item is assumed to be exponentially distributed. The Gaver algorithm is used to obtain the stationary probability vector of the system in the steady-state. Further, the necessary numerical interpretations are investigated to enhance the proposed model.

Customer Acquisition and Retention: A Fluid Approach for Staffing

We investigate the trade‐off between acquisition and retention efforts when customers are sensitive to the quality of service they receive, that is, whether they get timely access to a company's resources when requested. We model the problem as a multi‐class queueing network with new and returning customers, time‐dependent arrivals, and abandonment. We derive its fluid approximation; a system of ordinary linear differential equations with continuous, piecewise smooth, right‐hand sides. Based on the fluid model, we propose a novel approach to determine optimal stationary staffing levels for new and returning customer queues in anticipation of future time‐varying dynamics. Using system accessibility as a proxy for service quality and staffing levels as a proxy for investment, we demonstrate how to apply our approach to two families of time‐varying arrival functions motivated by real‐world applications: an advertising campaign and a clinical setting. In a numerical study, we demonstrate that our approach creates staffing policies that maximize throughput while balancing acquisition and retention efforts more effectively (i.e., equitable abandonment from each customer class) than commonly used near‐stationary methods such as variants of square‐root staffing policies. Our model confirms that acquisition and retention efforts are intimately linked; this has been found in empirical studies but not captured in the operations literature. We suggest that in time‐varying environments, focusing on either alone is not sufficient to maintain high levels of throughput and service quality.

Comment on Modified Fare Ratio in a Two-Class Static Revenue Management Model with Buy-up Behavior

We review the optimal booking limit in the two-class static revenue management model with customers’ buy-up behavior. This is when a deterministic fraction of the low-fare customer class that cannot book early are willing to book the higher fare later. This simple model with dependent demands is difficult to analyze. Some well-known publications, such as Talluri and van Ryzin ( 2004 ) and Phillips ( 2005 ), treat this model incorrectly. In this note, we correct an erroneous formula for the modified fare ratio with the proper probabilistic interpretation. The correction was established previously by Brumelle et al. ( 1990 ). Numerical examples reveal that the corrected modified fare ratio provides a lower optimal booking limit, resulting in a higher expected revenue than those obtained by using the incorrect modified fare ratio.

Algorithmic Analysis of Finite-Source Multi-Server Heterogeneous Queueing Systems

The paper deals with a finite-source queueing system serving one class of customers and consisting of heterogeneous servers with unequal service intensities and of one common queue. The main model has a non-preemptive service when the customer can not change the server during its service time. The optimal allocation problem is formulated as a Markov-decision one. We show numerically that the optimal policy which minimizes the long-run average number of customers in the system has a threshold structure. We derive the matrix expressions for performance measures of the system and compare the main model with alternative simplified queuing systems which are analysed for the arbitrary number of servers. We observe that the preemptive heterogeneous model operating under a threshold policy is a good approximation for the main model by calculating the mean number of customers in the system. Moreover, using the preemptive and non-preemptive queueing models with the faster server first policy the lower and upper bounds are calculated for this mean value.