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In this paper, we study a multi-server queueing system with retrials and an infinite orbit. The arrival of primary customers is described by a batch Markovian arrival process (BMAP), and the service times have a phase-type (PH) distribution. Previously, in the literature, such a system was mainly considered under the strict assumption that the intervals between the repeated attempts from the orbit have an exponential distribution. Only a few publications dealt with retrial queueing systems with non-exponential inter-retrial times. These publications assumed either the rate of retrials is constant regardless of the number of customers in the orbit or this rate is constant when the number of orbital customers exceeds a certain threshold. Such assumptions essentially simplify the mathematical analysis of the system, but do not reflect the nature of the majority of real-life retrial processes. The main feature of the model under study is that we considered the classical retrial strategy under which the retrial rate is proportional to the number of orbital customers. However, in this case, the assumption of the non-exponential distribution of inter-retrial times leads to insurmountable computational difficulties. To overcome these difficulties, we supposed that inter-retrial times have a phase-type distribution if the number of customers in the orbit is less than or equal to some non-negative integer (threshold) and have an exponential distribution in the contrary case. By appropriately choosing the threshold, one can obtain a sufficiently accurate approximation of the system with a PH distribution of the inter-retrial times. Thus, the model under study takes into account the realistic nature of the retrial process and, at the same time, does not resort to restrictions such as a constant retrial rate or to rough truncation methods often applied to the analysis of retrial queueing systems with an infinite orbit. We describe the behavior of the system by a multi-dimensional Markov chain, derive the stability condition, and calculate the steady-state distribution and the main performance indicators of the system. We made sure numerically that there was a reasonable value of the threshold under which our model can be served as a good approximation of the BMAP/PH/N queueing system with the PH distribution of inter-retrial times. We also numerically compared the system under consideration with the corresponding queueing system having exponentially distributed inter-retrial times and saw that the latter is a poor approximation of the system with the PH distribution of inter-retrial times. We present a number of illustrative numerical examples to analyze the behavior of the system performance indicators depending on the system parameters, the variance of inter-retrial times, and the correlation in the input flow.

Abstract A retrial queue with classical retrial policy, where each blocked customer in the orbit retries for service, and general retrial times is modeled by a piecewise deterministic Markov process (PDMP). From the extended generator of the PDMP of the retrial queue, we derive the associated martingales. These results are used to derive the conditional expected number of customers in the orbit in the transient regime.

Virtually all the sectors of economy such as finance, banking, hospitality and other businesses have grown up substantially in the past few years due to the growth of mobile service sector. From the inception of Reliance Jio in Madhya Pradesh, It has occupied a large number of customers in terms of no. of subscribers. This creates unrest among the telecom service operators operating in Madhya Pradesh. As the market moves forward, customer satisfaction becomes imperative for service firms to remain combative at marketplace. To study customer satisfaction, it is mandatory to study socio demographics of customers. Hence efforts have been made in this research paper to study the satisfaction level of customers from several demographic variables. This is a hypothetical research study in which primary data is collected from 500 active mobile users of Bhopal (MP), India. One way ANOVA and T-test were used to analyze the data through SPSS 21.0 software. Specific variables of American customer satisfaction index (ACSI) and European customer satisfaction index (ECSI) were being studied with different socio demographic variable of customers to move ahead in present research study. Significant difference was found in level of customer satisfaction with the age group and type of connection in telecom sector.

The purpose of this study is to determine the average level of customer arrivals and the average service time of customers in the queue. The analytical model used in this study is a multi-channel single-phase queuing theory analysis with a mathematical formula. The queuing process is a process related to the arrival of the customer to a queuing system, then waiting in the queue until the waiter selects the customer according to the service discipline, and finally the customer leaves the queuing system after the service is finished. At Bank Syariah Indonesia (BSI) KC Bengkulu S. Parman 1 there are 5 tellers provided to serve customers who will make deposits, withdrawals and cash transfers. Queues that occur at the optimal service level can be obtained by the performance of the queuing system with the calculation results, namely, the average number of customers in the queue (nq) 31.88 customers, customers in the total system 33.08 people, the average time in the queue 0, 000767 and the total system time is 0.034097 or 2 minutes. Thus, customers do not take too long to make transactions. With the number of tellers as many as five people, there is a long waiting time for customers (Wq) in the queue, which is 0.02777 hours or 2 minutes and the average number of customers in the queue (Ls) is 2 people..

The term ‘event marketing’ has been used in a range of different ways and given a range of different meanings. While all of these meanings may be appropriate in various contexts, the term utilized in this chapter refers to that part of the event management process that involves the marketing of events and hence, to the market research, promotion and advertising that aims at increasing the number of customers that pay to attend the event. The American Marketing Association defines marketing as “the set of activities, institutions, and processes for creating, communicating, delivering and exchanging offerings that have value for customers, clients, partners, and society at large” (www.ama.org). In this vein, event marketing includes the activities, tactics and tools used to communicate and promote the value of events to prospective attendees.

This study aims to investigate which hotels' attributes are most valued by the guests of the main markets of Porto. The guests' knowledge, preferences, and needs are crucial data that impact customer satisfaction. As a people-to-people industry, the hotel industry must consider the heterogeneity of its markets and invest in improving its services, considering the aspects they value. However, is the heterogeneity pronounced that much? Or are there any similarities between markets? Guests do not have similar satisfaction levels, so to guarantee the best experience for the most significant number of customers, these should be studied by market segments, once individual study would be impracticable. Through the comments made on the Booking.com, following the assumption that guests comment on what they value, the attributes that guests of different nationalities refer to Porto hotels have been collected. From the analysis of all the collected data, it can be concluded that all the main markets' value attributes and the fundamental differences are based on the hierarchy of these attributes.

This document addresses the problem of scheduling and routing a specific number of vehicles to visit a set of customers in specific time windows during a planning horizon. The vehicles have a homogeneous limited capacity and have their starting point and return in a warehouse or initial node, in addition, multiple variants of the classic VRP vehicle routing problem are considered, where computational complexity increases with the increase in the number of customers to visit, as a characteris-tic of an NP-hard problem. The solution method used consists of two connected phases, the first phase makes the allocation through a mixed-integer linear programming model, from which the visit program and its frequency in a determined plan-ning horizon are obtained. In the second phase, the customers are grouped through an unsupervised learning algorithm, the routing is carried out through an Ant Colony Optimization metaheuristic that includes local heu-ristics to make sure com-pliance with the restrictive factors. Finally, we test our algorithm by performance measures using instances of the literature and a comparative model, and we prove the effectiveness of the proposed algorithm.

The emergence of the COVID-19 pandemic in early 2020 had a major impact on human life on a global scale. Many actions and policies are aimed at anticipating transmission and breaking the chain of the spread of the COVID-19 virus, thus requiring store owners to implement various health protocols. This study discusses the monitoring system for the condition of the storeroom in real-time with the IoT concept, and the implementation of Sugeno fuzzy logic in controlling the speed of the exhaust fan motor to circulate air in the room and limit the number of customers during the COVID-19 pandemic based on conditions of temperature, humidity, and many people in the storeroom. The actual test results from the implementation of Sugeno fuzzy logic show that the system has good performance in controlling the speed of the exhaust fan and limiting the number of customers based on the level of danger of the potential COVID-19 transmission in the room automatically and can monitor the condition of the room through the Thinger.io website in real time.

The stochastic approximation procedure with delayed groups of delayed customers is investigated. The Robbins-Monro stochastic approximation procedure is adjusted to be usable in the presence of delayed groups of delayed customers. Two loss systems are introduced to get an accurate description of the proposed procedure. Each customer comes after fixed time-intervals with the stage of the following customer is accurate according to the outcome of the preceding one, where the serving time of a customer is assumed to be discrete random variable. Some applications of the procedure are given where the analysis of their results is obtained. The analysis shows that efficiencies of the procedure can be increased by minimizing the number of customers of a group irrespective of their service times that may take maximum values. Efficiencies depend on the maximum service time of the customer and on the number of customers of the group. The most important result is that efficiencies of the procedure are increased by increasing the service time distributions as well as service times of customers .This new situation can be applied to increase the number of served customers where the number of served groups will also be increased. The results obtained seem to be acceptable. In general, our proposal can be utilized to other stochastic approximation procedures to increase the production in many fields such as medicine, computer sciences, industry, and applied sciences.

When the required number of customers is available in the general bulk service (GBS) queueing system, the server begins service. Otherwise, the server will remain inactive until the number of consumers in the queue reaches that minimum required number. Customers that have already come must wait throughout this time, regardless of their arrival time. In some circumstances, like specimens awaiting testing in a clinical laboratory or perishable commodities awaiting delivery, it is necessary to finish services before the expiration date. It might only be achievable if consumers’ waiting times are kept under control. As a result, the flexible general bulk service (FGBS) rule is developed in this article to provide flexibility in batching. The effectiveness of FGBS implementation has been demonstrated using two examples: a clinical laboratory and a distribution center. To justify the suggested model, a simulation study and numerical illustration are provided.