Service Times Of Customers Research Articles

Application of Queue Theory in Cafe Services with Erlang Distribution

As urban lifestyles evolve, culinary businesses, particularly cafes, have experienced rapid growth. This surge in popularity has led to an increase in customers and, consequently, longer queues. These extended wait times can frustrate customers and pose challenges to cafe management. To address this issue, we conducted a comprehensive eval___uation and optimization of the service system at a Samarinda cafe using the Erlang distribution queuing system. Primary data was meticulously collected over six days, amounting to a total of 12 hours of observation. Kolmogorov-Smirnov distribution fitting tests were employed, revealing that customer service times adhered to an exponential distribution. The average customer arrival rate was determined to be 0.351 per minute, while the average service time was calculated at 5.546 minutes per customer. Our analysis confirmed that the system operates in a steady state with a utility value of 0.06, indicating sufficient service capacity to handle the current customer load. Therefore, the study concludes that the cafe's service system is currently optimal.

단수 휴가와 일량 제어정책을 갖는 이산시간 Geo/G/1 시스템의 대기시간 분석

In this paper, we derived the steady-state waiting time distribution of a discrete-time Geo/ G/1 queuing system under single vacation and D-policy. Customers such as WIP(work-in- process), parts, packets arrive at the system with Bernoulli process, and the server takes a single vacation with length of V when there are no more customers to service in the system. The restart condition is met when the total service time (workload, unfinished work) of customers waiting in the system at the end of vacation exceeds the workload threshold D. If the total amount of work in the system is less than or equal to D at the end of vacation, the server waits until the restart conditions are met and serves waiting customers. Otherwise, it starts to be busy as soon as the vacation ends. The average waiting time was also derived as a performance measure. Additionally, the computability of theoretical results was confirmed through a numerical example. The server control policy covered in this study can be applied in situations where it is desired to reduce operating costs per unit time due to high server restart costs (or energy consumption) in production and communication systems.

Optimizing Restaurant Queue Management: A Simulation-Based Approach Using Arena Software

Examining the effectiveness of models in terms of utilization and waiting time is one of the anticipated benefits of analyzing queuing systems. This study uses Arena simulation software to examine the queue system of a particular restaurant. The primary objective is to assess and enhance the restaurant’s service efficiency through the modelling of customer arrivals, service procedures, and queue dynamics. Data on customer arrivals and service times were collected for the restaurant’s current system. The necessary expressions were developed from the observed data using the input analyzer. A conceptual model of the original queuing system was created, and two alternative Arena models were developed to reduce customer waiting times in the restaurant. The developed models were run to evaluate their performance. During a 24-hour simulation study, the average waiting time in the overall model was found to be 24.49 minutes, with a maximum of 48.69 minutes. The waiting time for server 1 was 25.30 minutes, for server 2 was 23.27 minutes, for server 3 was 25.11 minutes, and for server 4 was 22.30 minutes. The number of customers in line at server 1 was 12.65, at server 2 was 6.98, at server 3 was 8.29, and at server 4 was 8.25. Resource utilization was 57% for server 1, 35% for server 2, 27% for server 3, and 15% for server 4. By decreasing the queuing length and average waiting time in the restaurant, customer satisfaction can be increased, leading to a reduction in time wasted. The findings indicate significant potential for improving overall service quality and reducing client wait times. This research provides valuable insights for restaurant managers seeking to enhance customer satisfaction and operational efficiency.

Exploring logistics transport route optimization: An algorithmic study based on RFID technology

With the rapid growth of e-commerce, logistics companies face challenges in efficient routing and scheduling to meet dynamic delivery demands. This paper proposes a novel logistics scheduling model to optimize vehicle routing using Radio Frequency Identification (RFID) technology. A vehicle scheduling model is developed. The random customer demand and service time are solved using an adaptive taboo search algorithm combined with a nearest neighbor algorithm. Comparative experiments demonstrate the performance of the improved method in completing tasks and reducing queueing time compared to other methods. A case study of route optimization for a logistics company shows the model can recommend optimized routes that reduce total transportation cost by over 25% compared to using RFID alone. The results highlight the potential of the proposed technique to enhance logistics efficiency. Limitations and future work are discussed.

Construction of block diagrams of a simulation model of the customer service process

The article, which is part of the author’s dissertation research, is devoted to the construction of a simulation model, namely a discrete-event model of the customer service process «as is» and «as will be». The introduction substantiates the relevance of the research topic, highlighting the object and subject of the study. A hierarchical structure of the system of quality indicators for infocommunication services has been constructed. There are 4 levels of indicators, at each level quality indicators are highlighted, namely: service speed indicators (average service time for a technical fault, average response time for reference services); satisfaction indicators (percentage of calls regarding technical aspects of service, percentage of calls regarding organizational aspects of service) and others. A hypothesis has been put forward about a change in the state of the service process after the introduction of a functional dialog agent into the process, which involves a reduction in customer service time. To test the hypothesis about reducing customer service time, discrete-event simulation models of the process «as is» and «as will be» were built, since modeling in terms of queuing theory not only improves the understanding of existing processes in the company, but also helps to identify bottlenecks and identify areas for further optimization, which ultimately leads to increased customer satisfaction and the efficiency of the company as a whole. Within the framework of the developed discrete-event model, the main attention is paid to two main stages: modeling the receipt of requests and modeling the processing of requests. Process optimization includes the introduction of an automated diagnostic system, namely a functional conversational agent to reduce wait time and increase request processing throughput. Block diagrams of discrete-event simulation models of the service process were also constructed in terms of the AnyLogic environment, and the advantages of its use were highlighted. The main objects used to create discrete-event models that describe the mathematical state of the simulated system are presented.

Analisis Sistem Antrian pada Proses Pelayanan Konsumen di Warung Ayam Geprek Najwa Menggunakan E-WOM

This study aims to determine the effect of e-Wom, food quality and service quality on Purchase Satisfaction at Najwa geprek chicken stall. This research method was quantitative through an online questionnaire with a total of 145 respondents. The data used for the analysis of this queuing system is primary data, which is in the form of customer arrival time data and service time data (server), for time measurement carried out using the help of a stopwatch. The results of data analysis showed that the enthusiasm of Rantauprapat residents towards Najwa geprek chicken stall was very high, this made Najwa geprek chicken stall does not empty of visitors, resulting in queues

Bayesian analysis of Markov modulated queues with abandonment

AbstractWe consider a Markovian queueing model with abandonment where customer arrival, service and abandonment processes are all modulated by an external environmental process. The environmental process depicts all factors that affect the exponential arrival, service, and abandonment rates. Moreover, the environmental process is a hidden Markov process whose true state is not observable. Instead, our observations consist only of customer arrival, service, and departure times during some period of time. The main objective is to conduct Bayesian analysis in order to infer the parameters of the stochastic system, as well as some important queueing performance measures. This also includes the unknown dimension of the environmental process. We illustrate the implementation of our model and the Bayesian approach by using simulated and actual data on call centers.

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.

Exploring the Potential of Cyber Manufacturing System in the Digital Age

Cyber-manufacturing Systems (CMS) have been growing in popularity, transitioning from conventional manufacturing to an innovative paradigm that emphasizes innovation, automation, better customer service, and intelligent systems. A new manufacturing model can improve efficiency and productivity, and provide better customer service and response times. In addition, it may revolutionize the way products are produced, from design to completion. Therefore, it is likely that this new manufacturing model will become increasingly popular. By building new technologies on top of existing CMS, these systems will ensure that data exchange and integration between decentralized systems are reliable and secure. Recently published case studies from industry and the literature support this claim; some challenges remain to be overcome. In general, the use of CMS can revolutionize the manufacturing industry. This study comprehensively analyzes these systems and their potential applications and implications. An overview of the field is then given and various aspects of CMS are also explored with more details. A taxonomy of the most common and current approaches to CMS is presented, including networked cyber-manufacturing systems, distributed cyber-manufacturing systems, cloud-based cyber-manufacturing systems, and cyber-physical systems (CPS). Furthermore, our survey identifies several popular open-source software and datasets and discusses how these resources can reduce barriers to CMS research. In addition, we identify several important issues and research opportunities associated with CMS, including better integration between hardware and software, improved security and privacy protocols, communication protocols, and improved data management systems. In summary, this paper presents a comprehensive overview of current technology and valuable insights are provided for the potential impact of CMS on society and industry.

Understanding the joint effects of internal and external anthropomorphic cues of intelligent customer service bot on user satisfaction

As one specific type of chatbot, Intelligent Customer Service Bot (ICSB) satisfies users by providing uninterrupted customer service and reducing response time. However, users still prefer to interact with humans rather than robots. In previous studies, scholars have focused more on enhancing the anthropomorphic characteristics of chatbot by treating anthropomorphic characteristics as a general concept. Few literatures have studied the influence of both external and internal features on user satisfaction and the possible interactive effects between the two dimensions of chatbot anthropomorphic cues. Therefore, this paper studies the main effects of internal anthropomorphic constructs (cognitive empathy and emotional empathy) and external anthropomorphic constructs (virtual appearance) of ICSB on user satisfaction, as well as the two-way and three-way interaction effects among them. With a scenario-based survey of 331 respondents, the results confirm the hypotheses about the main effects, the two-way and three-way interaction effects in the model.

Deep Reinforcement Learning for Truck-Drone Delivery Problem

Utilizing drones for delivery is an effective approach to enhancing delivery efficiency and lowering expenses. However, to overcome the delivery range and payload capacity limitations of drones, the combination of trucks and drones is gaining more attention. By using trucks as a flight platform for drones and supporting their take-off and landing, the delivery range and capacity can be greatly extended. This research focused on mixed truck-drone delivery and utilized reinforcement learning and real road networks to address its optimal scheduling issue. Furthermore, the state and behavior of the vehicle were optimized to reduce meaningless behavior, especially the optimization of truck travel trajectory and customer service time. Finally, a comparison with other reinforcement learning algorithms with behavioral constraints demonstrated the reasonableness of the problem and the advantages of the algorithm.

Correlated Queues with Inter-Arrival Times Depending on Service Times

We consider a type of correlated queue in which the inter-arrival time between two consecutive customers linearly depends on the service time of the first customer. We first derive infinite systems of linear equations for the moments of the waiting time in two special cases, based on which we then develop several methods to calculate the moments of the waiting time by using MacLaurin series approximation, Padé approximation and truncation method. In addition, we show how the moments and covariances of the inter-departure times of the correlated queue can be calculated based on the moments of the waiting time. Finally, extensive numerical examples are provided to validate our methods.

시뮬레이션 방법에 의한 보조재생함수의 근사

It is known that it is very difficult to calculate the auxiliary renewal function in most cases. We propose three methods of approximating the auxiliary renewal function by simulaion. At first, we review some theoretical results on M/G/1 queueing model with impatient customers, and observe that the auxiliary renewal function is included in the results. Then we propose three ideas by which we can approximate the auxiliary renewal function by simulation method, and give some approximated value of the function when the service time of customers are ditributed to Weibull and uniform distribution and constant vaule. It is found that three methods by simulation give almost same estimate for auxliliary renewal function with very small standard errors in one million repetition of simulation and the graph of the auxiliary renewal function can be showed. Finally, we conclude that any method given in this paper is acceptable and reliable if the simulation is carried with sufficiently many repetition.

Multi-Class, Multi-Server Queueing Inventory System with Batch Service

In this paper, we consider a queueing inventory system with batch arrival and batch service processes. Customers arrive in batches of sizes 1,2,…,k, according to a marked compound Poisson process. We call a batch of customers as belonging to j when there are j individual customers in that batch. The service facility has waiting rooms for each category of customers and also a room to serve them. Except for category 1, all other customers have finite waiting rooms. The service room has only a limited number of seats. These seats are arranged in such a fashion that customers belonging to category j have groups of seats, each with j seats for j=1,2,…,k. Customers are taken for service according to the availability of seats designated to each category. A category j customer can be taken for service only if j items are available in the inventory. The service time of customers of category j is exponentially distributed with parameter depending on j for j=1,2,…,k. The number of seats available in the service room for each category of customers is restricted to a finite number. The replenishment for items follows the (s,S) policy: fill up to S at the time of replenishment. Lead time follows an exponential distribution. We analyze the system in the equilibrium state. Performance characteristics are evaluated and a number of numerical illustrations are provided.

An Improvement in Power Quality and By-Product of the Run-Off River Micro Hydro Power Plant

Utilization of Micro Hydro Power Plant at the Gunung Halu case study type run-off the river is a household use only in the afternoon, around 5 pm until bedtime at about 10 pm. Therefore, more than 75% of the energy is lost. This case study lost power which can be used as a by-product, such as for drying coffee beans. In this case study, a design was carried out to obtain by-products and improve power quality in the electrical system. In addition, they complain about the poor quality of power controlled by frequency using Triac-Based Electronic Dummy Load Control. The heat from the dummy load in the case study is used as a by-product. MHP with a minimum power of 20 kW, and the usage time of customer service is about 6 h. The energy for the by-products is about 360 kWh/day, and the power quality improved by using Triac-Based Electronic Load Control and Hysteresis Current Control for the active filter. As a result, the power factor is close to one, the generator current harmonics is less than 2%, and the voltage harmonics is less than 5%.

Periodic Vehicle Routing Problem with Driver Consistency and service time optimization

The Periodic Vehicle Routing Problem with Driver Consistency is an extension of the classic Vehicle Routing Problem in which routes for several vehicles have to be determined over a time horizon of several days. Each customer has an associated set of possible visit schedules and must be visited always by the same vehicle. In this paper, we study a variant of the PVRP-DC in which, in addition to routes and visit schedules, service times of customers have to be determined in order to maximize the utility of the service to the company. We call this problem the Periodic Vehicle Routing Problem with Driver Consistency and Service Time Optimization. We present a mixed-integer linear programming formulation for the problem, propose three branch-and-cut methods to solve it, two of which are based on Benders reformulations, and report computational results on benchmark instances with different features.

Feeder delivery vehicle scheduling optimization of high-speed railway express based on trunk and branch intermodal transportation

In view of the traditional branch line end express delivery centralized mode cannot adapt to the growing demand of high-speed rail (HSR) express, resulting in poor connection between trunk and branch line, high cost and poor timeliness. In this paper, the problem of scheduling optimization of branch-line flexible distribution vehicles relying on intermodal transportation of trunk and branch lines is proposed. Considering the number of vehicles, vehicle capacity, customer service time window and other constraints, an integer linear programming mathematical model with the minimum total cost of vehicle transportation cost, usage cost and time window penalty cost as the optimization objective is established. A two-level nested heuristic algorithm with two-level coding structure is proposed to solve the problem. Finally, a simulation example is given to verify the effectiveness of the model and the algorithm. The results show that the vehicle scheduling optimization problem studied in this paper can effectively improve the timeliness and accuracy of HSR express delivery, and can significantly reduce the total vehicle delivery cost.

Business Cost Modelling of Information Processing in Supply Chain Units

The paper analyzes and successively assesses the problem of information delays in a sample logistics system, in which customer inquiries are sent to adjacent or dedicated units in the logistics chain. Within such a framework time and unit costs of customer service and inquiry are analyzed. A detailed model of the logistics system is thus elaborated using a mathematical approach and its graphical representation. The accompanying case study includes the analysis of the detailed situation in which two models are compared that do not differ in the structure of logistic units but are characterized by different information flow paths. Simulation results are presented through a thorough graphic, numerical and descriptive analysis. Finally, the problem of information transmission in the logistics system is summarized.

A PH i /PH i , n / C / C Queuing Model in Randomly Changing Environments for Traffic Circulation Systems

Robust optimal design of circulation systems (e.g., roads for vehicles or corridors for pedestrians) relies on an accurate steady-state traffic flow model that considers the effect of randomly changing environmental factors (e.g., daily periodicity and weather). Most analytical models assume that the customer interarrival time and service time of circulation facilities follow the exponential distribution with fixed rate parameters, which is unrealistic in most cases. In this paper, we develop a stationary PH i /PH i , n / C / C state-dependent queuing model in a randomly changing environment (RE), which is represented by a Markov chain. The model simultaneously considers the general randomness of arrival and service, the randomly varying rate parameters, and the state-dependent service (the travel time increases with the number of customers). The existing matrix analytic scheme (MAS) algorithm is extended to solve the proposed model because it avoids the explicit calculation of probability distributions. The space complexity of the algorithm is only linear in the number of RE states and is independent of the enormous (four-dimensional) state space of the Markov process. Its time complexity is a linear function of the product of the queue capacity and the number of RE states. Our model is validated versus simulation estimates. The obtained conditional performance measures can accurately capture the queue accumulation and dissipation and reveal the effect of randomly changing environments. Numerical experiments provide some interesting findings. (1) The proposed stationary model coincides with the transient M( t )/G x / C / C fluid queuing model under special conditions. (2) Under high traffic intensities, increasing the randomness in the duration time of the RE state leads to an obvious growth in the conditional queue length. (3) An increase in the facility length leads to an increase or a decrease in the average output rate, depending on whether the congestion dissipates effectively in one cycle. (4) A larger width is required to obtain the maximum average output rate for traffic demand with a greater nonuniformity.

Optimizing driver consistency in the vehicle routing problem under uncertain environment

This paper investigates the construction of routes over multiple days while maintaining driver consistency, which requires that the multi-day service of each customer be provided by as few different drivers as possible over a planning horizon. Furthermore, if one customer is assigned to different drivers over multiple days, it is desirable that services are provided by one driver on as many days as possible. To optimize this driver consistency, a new quantitative measure of driver consistency is defined. In the proposed vehicle routing problem with driver consistency, driver consistency is modeled in the objective function. Another contribution is that we model the vehicle routing problem with driver consistency considering uncertainties in customer demands, travel times, and service times. Uncertain programming models for the considered problem are developed utilizing uncertainty theory. A hybrid algorithm with large neighborhood search and simulated annealing is designed to address the proposed NP-hard problem. Computational experiments are conducted on several datasets to highlight the performance of the proposed approach and the models. The impacts of uncertainty and the trade-off between the total travel time and driver consistency are also analyzed to reveal some managerial insights.Our analysis shows that uncertainty has negative impacts on minimizing total travel time while can improve driver consistency in some cases; Remarkable reduction in the total travel time can be achieved with little damage on driver consistency; However, totally focusing on minimizing total travel time comes at the price of sacrificing driver consistency drastically.