Negative Customers Research Articles

Queuing-Inventory System with Catastrophes in the Warehouse: Case of Rare Catastrophes

A model of a single-server queuing-inventory system (QIS) with a limited waiting buffer for consumer customers (c-customers) and catastrophes has been developed. When a catastrophe occurs, all items in the system’s warehouse are destroyed, but c-customers in the system are still waiting for replenishment. In addition to c-customers, negative customers (n-customers) are also taken into account, each of which displaces one c-customer (if any). The policy (s, S) is used to replenish stocks. If, when a customer enters, the system warehouse is empty, then, according to Bernoulli’s trials, this customer either leaves the system without goods or joins the buffer. The mathematical model of the investigated QIS is constructed in the form of a continuous-time Markov chain (CTMC). Both exact and approximate methods for calculating the steady-state probabilities of constructed CTMCs are proposed and closed-form expressions are obtained for calculating the performance measures. Numerical evaluations are presented, demonstrating the high accuracy of the developed approximate formulas, as well as the behavior of performance measures depending on the input parameters. In addition, an optimization problem is solved to obtain the optimal value of the reorder point to minimize the expected total cost.

A new method for computing the sojourn times in the MAP/M/1 queues with three types of negative customers

ABSTRACT In this paper, we propose a new method for computing the sojourn times in the MAP/M/1 queueing systems with three types of negative customers due to three basic removal rules: the RCH, RCE and RCA. To this end, we first give a necessary and sufficient condition under which the system is stable by means of the mean drift technique. Then we obtain the queue size distributions and the average stationary queue lengths by using the matrix-analytic method. Based on this, we provide a new effective method for computing the average sojourn time of any arriving customer through using the first passage times and the PH distributions. Finally, we use some numerical examples to illustrate how the performance measures are influenced by some key system parameters.

带负顾客的Geo/Geo/1排队策略与服务定价研究

带负顾客的Geo/Geo/1排队策略与服务定价研究

Asymptotic analysis of a closed G-network with rewards

A closed exponential G-network with positive and negative customers is studied. In addition, the G-network under study generates a sequence of rewards or earnings associated with network transitions from one state to another. The total network reward is a random process governed by the probabilistic relations of the Markov process that determines the number of customers in the network nodes. The purpose of this paper is to asymptotically study the G-network with rewards under the assumption of a large number of customers. The main objective is to calculate the expected total reward of the G-network in the asymptotic case. It is proved that reward density function satisfies the generalized Kolmogorov backward equation. An ordinary differential equation for the expected reward that the G-network will earn in a time t if it starts in a given initial state, is derived.

Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies

We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival process and they can be queued in an infinite buffer. The service time of a consumer customer follows a phase-type distribution. The system receives negative customers which have Poisson flows and as soon as a negative customer comes into the system, he causes a consumer customer to leave the system, if any. One of two inventory policies is used in the systems: either (s,S) or (s,Q). If the inventory level is zero when a consumer customer arrives, then this customer is either lost (lost sale) or joins the queue (backorder sale). The system is formulated by a four-dimensional continuous-time Markov chain. Ergodicity condition for both systems is established and steady-state distribution is obtained using the matrix-geometric method. By numerical studies, the influence of the distributions of the arrival process and the service time and the system parameters on performance measures are deeply analyzed. Finally, an optimization study is presented in which the criterion is the minimization of expected total costs and the controlled parameter is warehouse capacity.

On a retrial queue with negative customers, passive breakdown, and delayed repairs

AbstractThis paper studies an M/M/1 retrial queue with negative customers, passive breakdown, and delayed repairs. Assume that the breakdown behavior of the server during idle periods is different from that during busy periods. Passive breakdowns may occur when the server is idle, due to the lack of monitoring of the server during idle periods. When the passive breakdown occurs, the server does not get repaired immediately and enters a delayed repair phase. Negative customers arrive during the busy period, which will cause the server to break down and remove the serving customers. Under steady-state conditions, we obtain explicit expressions of the probability generating functions for the steady-state distribution, together with some important performance measures for the system. In addition, we present some numerical examples to illustrate the effects of some system parameters on important performance measures and the cost function. Finally, based on the reward-cost structure, we discuss Nash equilibrium and socially optimal strategy and numerically analyze the influence of system parameters on optimal strategies and optimal social benefits.

Analysis of M/M/1 queueing systems with negative customers and unreliable repairers

In this article, we study the M/M/1 queueing systems with negative customers and unreliable repairers. The arrival of a negative customer causes the failure of the server, and the server is repaired immediately. The repairers may successfully repair the server with probability p, and the server continues to serve customers in the system. Otherwise, once the repair fails, the system will be cleared and all customers are forced to leave the system. By analyzing the quasi-birth-and-death process and using the probability generating function method, we obtain the steady-state probability and some performance measures of the system. Then, based on the reward-cost structure, we discuss the strategic behavior of customers and consider the equilibrium strategy. Finally, the effects of system parameters on the performance measures, individual benefit, and social benefit are analyzed by numerical examples.

Analysis of a Collision-Affected M/GI/1/ /N Retrial Queuing System Considering Negative Customers and Transmission Errors

This paper considers a retrial G-queue with collisions, transmission errors, and a finite number of sources, where service and repair time are both general distributions. The number of sources (terminals) is finite and a source cannot generate new requests until the channel (server) finishes its work, i.e., the rate at which new primary requests are generated varies inversely with the number of data frame (customer) in the system. A collision occurs when service requests arrive at a busy channel, and transmission errors prevent data frames from leaving the system after completing service. Two types of arrivals are considered. Negative customers will break down the system in the busy state and remove the customer under service. The application of our model is indicated, with a particular emphasis on communication networks such as the local-area networks (LAN) with CSMA/CD protocol. Recursive formulas have been derived to calculate the stationary joint distributions and the Laplace transform of reliability function by applying the discrete transformations method along with the supplementary variables technique (SVT). Furthermore, the comparative performance and reliability analysis have been conducted numerically. Numerical examples are provided to investigate the sensitivity of different parameters on performance measures and reliability indicators.

Single-Server Queuing-Inventory Systems with Negative Customers and Catastrophes in the Warehouse

In this paper, we studied single-server models of queuing-inventory systems (QIS) with catastrophes in the warehouse part and negative customers (n-customers) in service facility. Consumer customers (c-customers) that arrived to buy inventory can be queued in an infinite buffer. Under catastrophes, all inventory of the system is destroyed but customers in the system (on server or in buffer) are still waiting for replenishment of stocks. Upon arrival of n-customer one c-customer is pushed out, if any. One of two replenishment policies (RP) can be used in the system: either (s,S) or randomized. In the investigated QISs, a hybrid service scheme was used: if upon arrival of the c-customer, the inventory level is zero, then according to the Bernoulli scheme, this customer is either lost (lost sale scheme) or joining the queue (backorder scheme). Mathematical models of the investigated QISs were constructed as two-dimensional Markov chains (2D MC). Ergodicity conditions of the investigated QISs were obtained, and the matrix-analytic method (MAM) was used to calculate the steady-state probabilities of the constructed 2D MCs. Formulas for performance measures were found and the results of numerical experiments are presented.

Analysis of P2P network system based on two‐stage service and failure repairability

SummaryAlong with the rapid development of the information technology revolution, P2P technology has been more and more widely and deeply researched in the field of mobile wireless, and mobile P2P has become an emerging and popular research field. The particularity of the mobile environment has extremely high requirements on the P2P network topology, resource transition paths and network security. In this paper, a two‐stage queueing model with negative customers and asynchronous failure is established based on a hybrid mobile network model combining the semi‐distributed topology and the fully‐distributed topology. Using the matrix‐geometric solution and Gauss‐Seidel iterative method, the probability distribution of the network model in steady‐state is obtained, and expressions for performance indicators such as the average number of peers in the two stages are given. Numerical experiments were conducted using programming software to analyze the effect of parameters on each indicator. The optimal parameters were solved by constructing the average cost unit time function and social benefit function to provide decision foundation for the mobile P2P network model.

Dashed expectations in service experiences. Effects of robots human-likeness on customers’ responses

PurposeThere is growing interest in the use of human-like social robots, able to undertake complex tasks whilst building consumer engagement. However, further exploration is needed on the optimal level of humanoid appearance for service robots. In particular, the literature is limited with respect to mitigating disconfirmed expectations for robots high in human-likeness. This paper aims to address this gap by testing the effect of robot appearance, disconfirmed expectations and warmth (vs competence) on customers’ responses.Design/methodology/approachThe study adopts a mixed-method design by presenting a focus group (Study 1) that guides two laboratory experiments (Studies 2 and 3). Studies 2 and 3 test for the moderating effect of warmth (vs competence) and the mediating roles of perceived eeriness and disconfirmed expectations.FindingsThe findings show that a robot high (vs low) in human-likeness leads to higher negative customers’ responses, which is explained by disconfirmed expectations rather than perceived eeriness. However, when customers interact with a warm (vs competent) robot high in human-likeness, this negative effect vanishes.Research limitations/implicationsThe paper investigates boundary conditions and underlying mechanisms that affect customers’ experiences. Although the study adopts high realistic experiments, a limitation lies in not measuring customers’ actual behaviours in the field.Practical implicationsThis study provides new insights on how the appearance and characteristics of social robots influence the consumers’ experience. By doing so, this study offers managers actionable insights (i.e. enhancing warmth) to lessen the risk of disconfirmed expectations.Originality/valueThe paper offers new explanations as to why human-like robots can generate negative responses from customers. Moving beyond the “uncanny valley” hypothesis, this study shows the key role of disconfirmed expectations in explaining consumers’ negative responses towards humanoid robots. Moreover, it sheds light on the moderating role of warmth (vs competence), which can mitigate such negative effects.

Customers’ percepton of electromobility in the Czech Republic: Longtidunal study 2018 – 2022

The paper sheds a light on the issue of electromobility in the Czech market due to the continuously negative customers’ perception. The Czech society is skeptical regarding green transition to electromobility. According to a European survey, Czech people want to stay loyal to fuel engine in 50% (EIB, 2022). Businesses buy electric vehicles, to become more sustainable in the eyes of all stakeholders. They would like to have the right position in a supply chain, often connected to sustainable businesses. Paper discusses the interest of the Czech consumers towards the sustainable electromobility in Czechia. This paper aims to identify possible differences in Electrical Vehicles’s perception in time. The study provided 4 surveys from 2018 – 2022, and similar questions on consumers’ attitude towards electromobility were set in questionnaires during this time period. Study findings from show the tendency to buy Electrical Vehicles, to consider an Electrical Vehicles as an environmentally friendly car more than vehicle with fuel engine.

Game-theoretic analysis of the single vacation queue with negative customers

ABSTRACT We present a game-theoretic analysis of an M/M/1 queueing system with negative customers and single server vacation. Both positive and negative customers arrive according to a Poisson process and the server stars a vacation when the system is empty. Whenever a negative customer arrives, the positive customer being served (if any) is forced to abandon the system and the server suffers a breakdown, immediately after, a repair is required. During the repair process, positive customers are not allowed to join the system. Besides, they decide whether to join or to balk the system based on a reward-cost structure under four cases of different levels of information. We derive the equilibrium joining strategies of positive customers in each case. Specifically, we obtain the equilibrium threshold in the observable queue and mixed joining probability in the unobservable queue. Finally, the effects of different information levels and several parameters on the equilibrium threshold and mixed joining probabilities are illustrated by numerical examples.

Resource Retrial Queue with Two Orbits and Negative Customers

In this paper, a multi-server retrial queue with two orbits is considered. There are two arrival processes of positive customers (with two types of customers) and one process of negative customers. Every positive customer requires some amount of resource whose total capacity is limited in the system. The service time does not depend on the customer’s resource requirement and is exponentially distributed with parameters depending on the customer’s type. If there is not enough amount of resource for the arriving customer, the customer goes to one of the two orbits, according to his type. The duration of the customer delay in the orbit is exponentially distributed. A negative customer removes all the customers that are served during his arrival and leaves the system. The objects of the study are the number of customers in each orbit and the number of customers of each type being served in the stationary regime. The method of asymptotic analysis under the long delay of the customers in the orbits is applied for the study. Numerical analysis of the obtained results is performed to show the influence of the system parameters on its performance measures.

A transient analysis to the M(τ)/M(τ)/k queue with time-dependent parameters

Abstract This work considers the infinite multi-server Markovian queueing model with balking and catastrophes where the rates of arrivals, service, balking, and catastrophes are time dependent. The catastrophes arrive as negative customers to the system. The arrival of negative customers to a queueing system removes the positive customers. The catastrophes may come either from another service station or from outside the system. In this paper, we obtained the transient solution of this model using the approach of probability-generating function. Also, we derived an expression of transient probabilities in terms of Volterra equation of the second kind. Furthermore, we obtained a measure for time-dependent expected number of customers in the system.

A novel neutrosophic set based hierarchical challenge analysis approach for servicizing business models: A case study of car share service network

Servicization as a part of circular economy has a prominent role in operations management research by emphasizing the functionality of the products. Servicizing business model is a phenomenon that the products are converted into services for sale, or process of transforming the consumers into users. This newly introduced way of business is defined as a new opportunity for operations management by focusing on; the reliability and durability of the products against the extreme repeatedly use, coordination problems in conducting the business, risk of encountering unknown negative customers, and moral hazard in product usage, operational difficulties, and the degradation of the products. All of the aforementioned issues in implementing the servicizing business models constitute a research question with the high impact of COVID-19 pandemics. Since people avoid using public transportation, car share programs are highly in demand. In addition, there is an obvious research gap in challenge analysis of the car-sharing programs’ literature, an overall service network challenge analysis is missing in the field of study. Hence, the purpose of this study is proposing a novel neutrosophic set based hierarchical challenge analysis approach for the servicizing business models with a step by step guidance, and presenting a real world case study addressing a car sharing company’s entire service network. A practitioner can understand which challenge should be dealt with first, what is the inter-relationship structure of these challenges in a hierarchy, and what is the expected final result of these interactions. The study also contributes to the theoretical background by using neutrosophic sets to propose a novel interpretive hierarchical challenge analysis. In this research, the evaluation of truth and indeterminacy membership degrees of a neutrosophic set are gathered separately instead of applying the defined linguistic variable schemes. The case study is a contemporary field of study attracting attention of innovative entrepreneurs, since there is an increased demand of individual car driving due to the isolation requirement arisen from COVID-19 pandemics.

Analysis of BMAP/MSP/1 queue with MAP generated negative customers and disasters

This paper studies an infinite-buffer single server queueing model with negative customers and disasters. The ordinary (positive) customers arrive in the system according to the batch Markovian arrival process and join the queue for service. The negative customer and disaster are characterized by two independent Markovian arrival processes. A negative customer removes the positive customer undergoing service, if any, and a disaster makes the system empty by simultaneously removing all the positive customers present in the system. We obtain the steady-state vector generating function (VGF) of the distribution of the number of positive customers in the system at arbitrary epoch. Further, the inversion of the VGF is carried out using the roots method to obtain the distribution. Moreover, the probability vectors at post-departure and pre-arrival epochs are also obtained. The results obtained throughout the analysis are computationally tractable, as illustrated by few numerical examples. Finally, we discuss the impact of the correlation of the arrival process of negative customers and disasters on the performance of the system through some graphical representations.

Equilibrium Joining Strategies of Positive Customers in a Markovian Queue with Negative Arrivals and Working Vacations

We study the economic analysis of a single server Markovian queueing system with positive and negative customers and multiple working vacations. Both positive and negative customers arrive in the system according to a Poisson process. Upon arrival, positive customers acquire some system information and decide whether to join or to balk the system based on the acquired information and a linear cost-reward structure. Negative customers on arrival break the server and kill the positive customer in service. The server is immediately sent for repair, and no customers are allowed during a repair. The server takes multiple working vacations after serving all the positive waiting customers. We obtain the equilibrium strategies and social benefit of positive customers under four different information situations. Numerical experiments are presented to show the effects of model parameters and information levels on the equilibrium joining behavior of positive customers.

Particle Swarm Optimization and Maximum Entropy Results for MX/G/1 Retrial G-Queue with Delayed Repair

This paper examines an MX/G/1 retrial model with negative customers including the concepts of working vacation, Bernoulli feedback, delayed repair, state-dependent and multi-optional services. Such a queue is quite relevant in real world, for instance in computer systems, manufacturing organisations, packet-switching networks, telecommunication systems, etc. The arrival pattern of customers is according to Poisson distribution. The service is such that first essential service (FES) is provided to every customer and second optional service (SOS) is provided in k phases to those who wants to opt for the same. The negative customers may arrive during the time when the server is busy in serving a positive customer. This leads to breakdown of the server and thus the server has to be restored (repair) by the repair man. Some moments may be taken by the repair man to initiate the repair process, leading to delay in repair. In our work, firstly we have calculated performance measures like long run probabilities and orbit size along with some reliability indices. Then a relative study between the exact expected waiting time and approximate expected waiting time of the system is presented via maximum entropy approach. Also we perform cost optimization using particle swarm optimization (PSO method). Few numerical results are also provided.

Analysis of wireless sensor networks with sleep mode and threshold activation

In order to reduce the energy consumption of wireless sensor networks and control the workload of necessary topology maintenance, the sleep mode and the threshold activation process in the energy saving strategy are considered. Combining with practice, factors such as environmental interferences and physical damages are considered. A repairable M/M/2 vacation queueing model with negative customers, feedback, N-strategy and working breakdown is established. Using quasi birth-and-death process and Gauss-Seidel iterative method, the expressions of performance indicators are given. Then, using MATLAB software for numerical analysis, the influence of system parameters on performance indicators is analysed. Finally, the social optimal parameters are found by constructing benefit functions. Under certain conditions, when $$\lambda =0.64$$ and $${{\beta }_{1}}=1.1$$ , the social benefit F can take the maximum value $$F=12.7729$$ .