Balking Behavior Research Articles

Cost Analysis of a Finite Capacity Queue with Server Failures, Balking, and Threshold-Driven Recovery Policy

The study is on the cost dynamics which is concerned with finite queues in particular to susceptibility to server outages, threshold-driven recovery and Catastrophic events, but main focus is on balking behaviour of the customers. A thorough investigation of the financial implications of interruptions and efficacy to recovery strategies is done and to alleviate the impact of breakdowns, disasters and customer refusals the queue system designs through empirical research is conducted. Various recovery policies have been compared with the existing thresholds, and the study further endeavors to categorize the cost-effective approach to mitigate the economic concerns of server failures and catastrophic incidents. The study brings discernments on the expected development in the management of the queuing system along with the assistance in complete decision-making in cost efficiency and enhancement of the complete system performance.

Service Competition in Two-Tier Healthcare Markets with Heterogeneous Patients Balking

Recently, public and private providers within the two-tier healthcare market engage in a fierce competition for patients, which is significantly influenced by patients’ multifaceted sensitivities to delays and payments, particularly when patients’ potential balking is considered. However, existing literature studying the two-tier healthcare market often presupposes patients as homogeneous or one-dimensionally heterogeneous, and neglects their balking behavior. In stark contrast, this paper delves into the combined effects of patients’ delay- and payment-sensitive heterogeneities, alongside their joining and balking decisions, on the service competition dynamics within the two-tier healthcare market. Leveraging a game-theoretic framework, we initially derive subgame equilibria, both inclusive and exclusive of patient balking, uncovering that patient balking can lead to a subgame perfect Nash equilibrium in the presence of two-dimensional patient heterogeneity. Intriguingly, our findings further suggest that the non-profit public provider may, counterintuitively, curtail its service capacity despite budgetary adequacy, contradicting the conventional assumption that such providers would fully allocate funds towards patient care. Ultimately, from a patient welfare standpoint, we find heightened payment heterogeneity discrimination proves detrimental to patients, whereas increased differentiation in delay heterogeneity benefits them. This revelation underscores a pressing social issue inherent in the two-tier healthcare market model: It has the potential to exacerbate healthcare disparities rooted in economic inequalities within the population.

Equilibrium balking behavior of customers and regulation measures in a multi-server queue with threshold policy

ABSTRACT The equilibrium balking behavior of customers and some effective regulation measures in a multi-server queueing system with a threshold policy are mostly investigated in this paper. We consider four information levels: entirely visible, nearly visible, nearly invisible and entirely invisible. For each case, we compare the equilibrium and socially optimal balking strategies of customers, formulate pricing strategy and analyze the revenue of the system manager. It is found that no matter what information level, there always exist the optimal thresholds that maximize the optimal social welfare and the system manager’s revenue, respectively. Moreover, how much information the customers know has influence on the optimal social welfare. Such findings can provide guidance for the social planner to formulate pricing strategies, make appropriate threshold policies and decide what information should be disclosed to customers to improve the optimal social welfare.

Comparisons of customer balking behavior in observable queues with N policies and geometric abandonments

ABSTRACT This paper studies and compares customer balking behavior in some single-server observable queues with N policies and geometric abandonments. We focus on two types of N policies: the classic one and the modified one. Under the classic N policy, the server begins to take a vacation period as soon as the system becomes empty until there are N customers in the queue. On the other hand, under the modified N policy, the server takes multiple vacations until at least N customers are waiting in the queue when a vacation time ends. Abandonment opportunities occur during a whole vacation period, and customers decide independently and sequentially whether to renege. Comparing the two types of N policies, we realize that the residual time of the server's last vacation under the modified N policy indeed inhibits customers joining, whereas it may be more economic in practice if we take the whole system cost into consideration. As for the optimal N, under which the server is free of compensation, we observe that he should choose the modified N policy when the abandonment probability is much close to 1. Otherwise, he should choose the classic N policy.

Equilibrium analysis of cloud user request based on the Markov queue with variable vacation and vacation interruption

This paper considers the equilibrium balking behavior of customers in a single-server Markovian queue with variable vacation and vacation interruption, where the server can switch across four states: vacation, working vacation, idle period, and busy period. Once the queue becomes empty, the server commences a working vacation and slows down its service rate. However, this period may be interrupted anytime by the vacation interruption. Upon the completion of a working vacation, the server takes a vacation in a probability-based manner and stops service if the system is empty. The system stays idle after a vacation until a new customer arrives. The comparisons between the equilibrium balking strategy of customers and the optimal expected social benefit per time unit for each type of queue are elucidated and the inconsistency between the individual optimization and the social optimization is revealed. Moreover, the sensitivity of the expected social benefit and the equilibrium threshold with respect to the several parameters as well as diverse precision levels is illustrated through numerical examples in a competitive cloud environment.

An observational field study on the effects of changes in shadow contrasts and noise on cattle movement in a small abattoir

This observational field study examined the effect of changes in shadow contrasts on the floor and noise on balking behavior during handling. Seventy-four Bos taurus beef cattle were observed during handling at a small abattoir. Shadow contrast type (none, soft, sharp) was recorded during three stages of handling (unloading, lairage to single-file alley and into stun box). Cattle balking behavior (stop, put head down, back up) and aversive handling (electric prod, tail twist) were recorded for each shadow contrast type and the presence or absence of a noisy rendering truck. Sharp contrast shadows increased balking behavior compared to soft contrast shadows or none during unloading (X2 = 12.4, P < 0.001). The noisy truck increased balking behavior during handling from the lairage holding pens to the single-file alley (P < 0.001) and during movement into the stun box (P = 0.001). Sharp contrast shadows on the floor from lighting changes and noise from the truck increased balking behavior in cattle.

Design of coordination contract for quality control-based supply chain under consumer balking behavior with fuzzy environment

Considering the ubiquity of consumer balking behavior (CBB) in real-life economics and the importance of product quality control (QC) to supply chain (SC) competitiveness, this paper explores the SC coordination under both the QC and the CBB. Specifically, the consumer’s loss aversion behavior was illustrated at a fixed balking probability, and the SC models were created for centralized and decentralized decision-making modes. After that, the optimal strategies for the retailer and the manufacturer were identified, and the comparative static analysis was adopted to explore the effects of the CBB and QC on the optimal decision-making of the SC. The research results show that the QC-based SC under the CBB cannot be coordinated by wholesale price contract alone, but can be coordinated perfectly by this contract when the retailer shares the quality effort and the manufacturer shares the oversupply cost and analyzed through the fuzzy environment with the formulation. This finding sheds new light on the theory and application of wholesale price contract in SC coordination. Finally, the parameter sensitivity analysis was performed on balking probability and product qualification rate (PQR) through numerical experiments, which further discloses the impacts of the CBB and product QC on the optimal decision-making and profit of the SC.

Comparisons of customer behavior in Markovian queues with vacation policies and geometric abandonments

This paper mainly studies customers’ equilibrium balking behavior in Markovian queues with single vacation and geometric abandonments. Whenever the system becomes empty, the server begins a vacation. If it is still empty when the vacation ends, the server stays idle and waits for new arrivals. During a vacation, abandonment opportunities occur according to a Poisson process, and at an abandonment epoch, customers decide sequentially whether they renege and leave the system or not. We consider four information levels: the fully/almost observable cases and the almost/fully unobservable cases, and get the customers’ equilibrium balking strategies, respectively. Then we also get their optimal balking strategies for the almost observable and the almost/fully unobservable cases, and make comparisons of customer strategies and social welfare for the almost observable and the almost/fully unobservable queues with single vacation and multiple vacations. Because of abandonment, we find that the customers’ equilibrium threshold in a vacation may exceed the one in a busy period in the fully observable queues. However, it has little effect on their equilibrium threshold in the almost observable queues, although frequent abandonment opportunity arrival inhibits their optimal threshold. Interestingly, for the almost unobservable queues, customers who arrive in a busy period are not affected by reneging that happened in the previous vacation when they make decisions of joining or balking, whereas the social planner expects that the customers can take it into consideration for social optimization. In the fully unobservable queues, because of no information, possible reneging surely influences customers’ equilibrium and optimal balking behavior. For the almost observable and the almost/fully unobservable queues, the optimal social welfare is greater in the queues with single vacation than that in the queues with multiple vacations.

Transient Behavior of a Single-Server Markovian Queue with Balking and Working Vacation Interruptions

This paper studies the time-dependent analysis of an M/M/1 queueing model with single, multiple working vacation, balking and vacation interruptions. Whenever the system becomes empty, the server commences working vacation. During the working vacation period, if the queue length reaches a positive threshold value ‘k’, the working vacation of the server is interrupted and it immediately starts the service in an exhaustive manner. During working vacations, the customers become discouraged due to the slow service and possess balking behavior. The transient system size probabilities of the proposed model are derived explicitly using the method of generating function and continued fraction. The performance indices such as average and variance of system size are also obtained. Further, numerical simulations are presented to analyze the impact of system parameters.

Pooling and Balking: Decisions on COVID-19 Testing

The most important issue in the prevention and mitigation of the COVID-19 pandemic is, perhaps, testing. To increase the convenience and efficiency of testing, many countries have set up walk-in testing sites. One fundamental decision for local governments or authorities to make is, should they build fewer centralized walk-in or drive-thru testing site (with more manpower and therefore a higher service rate) or more decentralized testing sites (each with less manpower and therefore a lower service rate)? To make this decision, one needs to understand the benefits and/or drawbacks of pooling incorporating people's balking behavior. In this short paper, we build classic queueing models to analytically characterize how system performance measures such as the expected waiting time, the expected queue length, and the balking probability change with the service rate, under different values of the implied utilization. These performance measures not only indicate the productivity and efficiency of testing operations, but also influence the safety and well-being of people and society.

Supply chain coordination and decisions under effort-dependent demand and customer balking behaviour

Supply chain coordination and decisions under effort-dependent demand and customer balking behaviour

Optimal Control F-policy for M/M/R/K Queue with an Additional Server and Balking

The multi-server finite queueing model with balking under admission control of customers based upon F-policy is investigated. In order to reduce the balking behavior of the customers, there is the provision of one additional server so as to shorten the queue length formed by the customers in rush hour. The noble realistic feature of the proposed Markov model is to control the admission of customers based on the threshold level ‘F’ of the queue size. According to ‘F’ policy, no more customers can be accommodated once the system is full and then after the further admission of the customers is not acceptable until the queue size drops to the predefined threshold level ‘F’. Chapman–Kolmogorov equations have been framed and are solved by using the recursive technique to establish the steady-state queue size probability distribution of the customers present in the system. A numerical example is taken to explore the various system indices. Adaptive neuro-fuzzy inference system (ANFIS) approach is applied to compare the soft computing results obtained by ANFIS with the results computed by the analytical method. The cost function is framed to determine the optimal control parameters namely threshold value ‘F’, the capacity of the system, the number of servers and service rate.

Variant impatient customers in an M/M/1 queue with balking re-service and Bernoulli multiple vacations

ABSTRACTThe impatient behavior of customers’ plays a vital role in the growth of the economy of a country. Customers leaving the queue, before getting served due to impatience, lead to heavy loss in trading centers. So, it is very important to study and analyze the impatient behavior of customers in various queueing models. A mathematical analysis of one such model is presented in this present research work. This paper analyzes the transient behavior of an M/M/1 queue with Bernoulli multiple vacations, balking, re-service and variant impatient customers. As soon as the server becomes free, he resumes Bernoulli multiple vacations. That is, the server commences either multiple vacations or multiple working vacations. During vacations and working vacations, the customers possess balking behavior. During working vacations, as the service speed is low, the customers waiting in the queue become impatient due to the huge waiting time. But, the customer who gets the service in slow service rate does not become impatient. After the completion of service, the customers may demand re-service during the busy periods. The transient system size probabilities, mean and variance are derived. Further, numerical simulations are provided to analyze the influence of various parameters of the system.

Supply Chain Coordination and Decision under Effort-Dependent Demand and Customer Balking Behavior

The paper explores supply chain coordination under a sales effort-dependent demand and customer balking scenario and analyses the impacts of revenue- and cost-sharing contracts on the decisions of supply chain members. This paper subsequently develops a two-echelon supply chain consisting of one supplier and one retailer and examines two models that incorporate customer balking and sales efforts: in one model, the retailer offers a revenue sharing-only contract, and in the other model, the retailer and the supplier bargain on the revenue and cost-sharing contract. The results show that the revenue- and cost-sharing contract can coordinate the decentralised supply chain better than it can coordinate a centralised supply chain and that the effects of customer balking on the supply chain are clear; when customer balking occurs, the probability of a sale occurring can increase the profit of the supply chain, while the threshold of inventory and the sales effort can improve the marketing demand.

Coordination of vendor managed inventory supply chain with price-sensitive demand under consumer balking behaviour

Coordination of vendor managed inventory supply chain with price-sensitive demand under consumer balking behaviour

Trade credit model with customer balking and asymmetric market information

Customer balking exists in many industries, and would significantly impact the supply chain management. We consider trade credit, customer balking behavior and market information asymmetry and information sharing in a two-level supply chain. Stackelberg equilibriums are derived in each scenario, respectively. The wholesale price and order quantity at equilibrium decrease (increase) in balking threshold (balking probability) when the production cost is not relatively low. The retailer benefits from the manufacturer’s pessimism with information asymmetry, while the optimism with information sharing. However, information asymmetry always harms the manufacturer. We design an information-dependent-credit-limited contract to enforce the retailer to share information.

A note on the optimal pricing strategy in the discrete-time Geo/Geo/1 queuing system with sojourn time-dependent reward

This work studies the optimal pricing strategy in a discrete-time Geo/Geo/1 queuing system under the sojourn time-dependent reward. We consider two types of pricing schemes. The first one is called the ex-post payment scheme where the server charges a price that is proportional to the time a customer spends in the system, and the second one is called ex-ante payment scheme where the server charges a flat price for all services. In each pricing scheme, a departing customer receives the reward that is inversely proportional to his/her sojourn time. The server should make the optimal pricing decisions in order to maximize its expected profits per time unit in each pricing scheme. This work also investigates customer's equilibrium joining or balking behavior under server's optimal pricing strategy. Numerical experiments are also conducted to validate our analysis.

Equilibrium and optimal balking strategies of customers in unobservable queues with double adaptive working vacations

This paper studies the customers’ equilibrium and socially optimal balking behaviour in some single-server Markovian queues with double adaptive working vacations. Once the system becomes empty, the server takes a working vacation with a low service rate. If there are customer arrivals during this period, a regular busy period begins as soon as he finishes the vacation. Otherwise, he takes another working vacation with a much lower service rate than that in the first working vacation. After completing the second vacation, the server either stays idle or begins a busy period. We discuss two types of unobservable queues: the almost unobservable queues and the fully unobservable queues, respectively, and arriving customers can’t observe system occupancy in both cases. For each type of queues, we get both the customers’ equilibrium and socially optimal balking strategies and make numerical comparisons between them. We observe that their positive and stable equilibrium strategy and optimal strategy are unique, and especially, the customers’ actual arrival rates in equilibrium in vacation states are not necessarily smaller than that in busy state in the almost unobservable queues. Moreover, we also find that whether the system information should be revealed to customers depends on the potential demand arrivals.

Equilibrium balking strategies of customers in Markovian queues with two-stage working vacations

This paper studies the customers’ equilibrium balking behavior in some single-server Markovian queues with two-stage working vacations. That is, the server starts taking two successive working vacations when the system becomes empty, during which he provides low-rate service but maintains different service rates in the two-stage vacations. Based on different precision levels of system information, we discuss observable queues, partially observable queues and unobservable queues, respectively. For each type of queues, we get the customers’ equilibrium balking strategy and equilibrium social welfare per time unit, and numerically observe that their positive equilibrium strategy is unique. Especially, for partially observable queues, the customers’ equilibrium joining probabilities in vacation states are not necessarily smaller than that in busy state.

Optimal balking strategies in an M/G/1 queueing system with a removable server under N-policy

In this paper, we consider the balking behavior of customers in anM/G/1 queueing system with a removable server under N-policy, wherethe server may be turned off when no customers are present, and beturned on when the queue length reaches size $N$. Arriving customersdecide whether to join the system or balk, based on a linearreward-cost structure that incorporates their desire for service, aswell as their unwillingness for waiting. For the unobservable andpartially observable queues, we first analyze the stationarybehavior of the system; then derive the equilibrium mixed strategiesand compare them to the socially optimal strategies. We take thenumber $N$ as a decision variable and discuss the optimal operationspolicy in equilibrium states. Finally, we present two examples todemonstrate some of the phenomena in the considered models.