Arrival Process Of Customers Research Articles

Online Learning for Constrained Assortment Optimization Under Markov Chain Choice Model

Assortment optimization finds many important applications in both brick-and-mortar and online retailing. Decision makers select a subset of products to offer to customers from a universe of substitutable products, based on the assumption that customers purchase according to a Markov chain choice model, which is a very general choice model encompassing many popular models. The existing literature predominantly assumes that the customer arrival process and the Markov chain choice model parameters are given as input to the stochastic optimization model. However, in practice, decision makers may not have this information and must learn them while maximizing the total expected revenue on the fly. In “Online Learning for Constrained Assortment Optimization under the Markov Chain Choice Model,” S. Li, Q. Luo, Z. Huang, and C. Shi developed a series of online learning algorithms for Markov chain choice-based assortment optimization problems with efficiency, as well as provable performance guarantees.

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.

Fight inventory shrinkage: Simultaneous learning of inventory level and shrinkage rate

In 2020, inventory shrinkage eroded $61.7 billion profit in the U.S. retail industry. Unfortunately, fighting inventory shrinkage to protect retailers' already slim profits is challenging due to unknown shrinkage rates and invisible inventory levels. While the latter has been studied in the literature, the former has not. To deal with this challenge, we introduce two new features to the Bayesian inventory models: (1) interleaving customer and theft arrival processes that contribute to actual sales and shrinkages, respectively, and (2) learning of both inventory level and shrinkage rate. We first derive the learning formulae using the triple‐censored sales data (invisible lost sales, shrinkages, and “lost shrinkages”) and then use them to construct a POMDP (partially observable Markov decision process) model for making inventory and loss prevention decisions. For a different level of information deficiency, we analyze the model property and design heuristic order policies to capture the benefit of learning. Through a numerical study, we show that our estimated shrinkage rate converges quickly and monotonically to the actual value. For products with high shrinkage rates (5–12%), our heuristic policy can help seize 82–94% of the ideal profit retailers could earn under full information. We note that feature (1) of our model is crucial. It not only reflects the actual arrival order but also allows us to learn the unknown shrinkage rate, which, in turn, can prevent serious underordering and vicious inventory cycles and can increase the profit by 108% in some cases. Our approach thus enables both effective inventory management and early identification of ineffective loss prevention strategies, reducing shrinkage, and increasing sales and profit.

The dwell point design of stereo garage conveyer considering load balance

By using the non-homogeneous characteristics of the customer arrival process and the characteristics of duration of stay in the garage, we predict the possible standby position of the vehicle conveyer for the next parking or pick-up task during the idle period of the garage and accomplish the design of the dwell point policy. By establishing a garage scheduling model and increasing the weight coefficient of energy consumption, we use the artificial colony algorithm to complete the optimization of the dwell point design policy to realize the load balance of each conveyer. The simulation results show that the average waiting time of customers and the average service time of conveyers are reduced by 20.2% and 62.7%, respectively, which indicates the effectiveness of the design strategy compared with the in-place standby strategy. The standard deviations of load balance of the non-optimized design strategy and the in-place standby strategy are both as high as 50 or more, which shows that the load is unbalanced; on the basis of the total energy consumption of conveyers and customer waiting time increased by 8.6% and 8.0%, respectively, the standard deviation of load balancing decreases by 98% for the optimized design strategy. The designed dwell point policy provides a new idea for improving the load balance of conveyer in stereo garage or warehouse system.

Simulation of non-homogeneous Poisson process of customer arrival in stereo garage

This paper studies the customer arrival process of stereo garage, considering both the Poisson process and non-homogeneous Poisson process for customer arrival. The relationship between average arrival rate and arrival time is obtained by regression analysis. By simulating different arrival processes, K-S test results are used to determine whether they belong to the same distribution as that of the actual arrival process. According to the actual operation process of stereo garage, two kinds of simulation programs under the arrival process are compiled. The simulation results show that the actual arrival process of customers in the garage is a non-homogeneous Poisson process. For the garage system with non-homogeneous customer source, non-homogeneous property is one of the reasons affecting its operation efficiency. This paper gives a reference for simulating the customer arrival process of such garage operation, and provides a new idea for improving the operation efficiency of the garage.

An Algorithm for Estimating the Expected Number of Customers for a Class of Markovian Queueing Systems

An algorithm is presented for estimating the expected number of customers for a class of Markovian queueing systems. The class is characterized by those systems whose transition matrix for the underlying customer arrival and departure process is finite, irreducible, and aperiodic. The algorithm does not depend on a closed-form solution for the limiting behavior of the queue. The expected number of customers is frequently used as a measure of effectiveness to describe the behavior of the system or to optimize its design or control. To calculate such a quantity one must usually obtain a closed-form expression for the steady-state probabilities. Unfortunately, of the myriad of Markovian queueing systems, only a few have known closed-form expressions for their steady-state probabilities. The most well-known, using Kendall’s notation, are the M/M/1 and the M/M/c system. The algorithm described below estimates the expected number in the system under steady-state without a need for closed form steady-state probabilities. All that is needed is the transition matrix for the underlying Markov chain.

On Two Interacting Markovian Queueing Systems

In this paper, we study a Markovian queuing system consisting of two subsystems of an arbitrary structure. Each subsystem generates a multi-class Markovian arrival process of customers arriving to the other subsystem. We derive the necessary and sufficient conditions for the stationary distribution to be of product form and consider some particular cases of the subsystem interaction for which these conditions can be easily verified.

Revenue management on an on-demand service platform

I consider a worker’s optimal per-unit-time pricing problem on an on-demand service platform. I establish that if the customer arrival process is Poisson, then any price discrimination must result only from differences in the customers’ willingness-to-pay distributions, and not from differences in their arrival or service-time characteristics. For multiple customer classes that differ in their willingness-to-pay distributions, I present a simple procedure to compute the optimal prices. Finally, I analyze price competition across workers in the presence of reputation effects.

Consumer Equilibrium, Demand Effects, and Efficiency in Group Buying

Group buying events, in which the unit price for a good or service declines with higher number of customer sign ups, are increasingly becoming popular for retailing goods and services, especially in emerging markets. This paper theoretically and empirically studies consumer equilibrium, pricing, and efficiency of these events. Modeling a continuous time customer arrival and sign-up process, we start by deriving the stochastic dynamic consumer equilibrium. Based on this equilibrium and utilizing sign-up level data from a major Chinese retailer's group buying events, we then structurally estimate consumer arrival rates and utility distributions for 266 events, and empirically verify the fit and predictive power of the model. Utilizing the estimated arrival rates and consumer utility distributions, we then employ a doubly stochastic two-stage Generalized Linear Regression Model to provide empirical evidence for consumer network effects in group buying, and estimate 16.6% increase in consumer demand attributable to the employment of a group buying mechanism. Through counterfactual analysis, we further estimate that employing group buying increased retailer profits by 11.1%, and with better price and discount selections, it can improve profits by more than 30% on average. We further demonstrate that the retailer is better off by setting low deal discounts for very low and very high consumer arrival rates, suggesting that a bell-shaped deal discount pattern as a function of consumer arrival rate is recommendable when employing group buying events.

Online Advance Scheduling with Overtime: A Primal-Dual Approach

Problem definition: We study a fundamental online resource allocation problem in service operations in which a heterogeneous stream of arrivals that varies in service times and rewards makes service requests from a finite number of servers/providers. This is an online adversarial setting in which nothing more is known about the arrival process of customers. Each server has a finite regular capacity but can be expanded at the expense of overtime cost. Upon arrival of each customer, the system chooses both a server and a time for service over a scheduling horizon subject to capacity constraints. The system seeks easy-to-implement online policies that admit a competitive ratio (CR), guaranteeing the worst-case relative performance. Academic/practical relevance: On the academic side, we propose online algorithms with theoretical CRs for the problem described above. On the practical side, we investigate the real-world applicability of our methods and models on appointment-scheduling data from a partner health system. Methodology: We develop new online primal-dual approaches for making not only a server-date allocation decision for each arriving customer, but also an overtime decision for each server on each day within a horizon. We also derive a competitive analysis to prove a theoretical performance guarantee. Results: Our online policies are (i) robust to future information, (ii) easy-to-implement and extremely efficient to compute, and (iii) admitting a theoretical CR. Comparing our online policy with the optimal offline policy, we obtain a CR that guarantees the worst-case performance of our online policy. Managerial implications: We evaluate the performance of our online algorithms by using real appointment scheduling data from a partner health system. Our results show that the proposed online policies perform much better than their theoretical CR, and outperform the pervasive First-Come-First-Served (FCFS) and nested threshold policies (NTPO) by a large margin.

Online Advance Scheduling with Overtime: A Primal-Dual Approach

We study a fundamental online resource allocation problem in service operations in which a heterogeneous stream of arrivals that vary in service times and rewards make service requests from a finite number of servers/providers. This is an online adversarial setting in which nothing more is known about the arrival process of customers. Each server has a finite regular capacity but can be expanded at the expense of overtime cost. Upon arrival of each customer, the system chooses both a server and a time for service over a scheduling horizon subject to capacity constraints. The system seeks easy-to-implement online policies that admit a competitive ratio (CR), guaranteeing the worst-case relative performance. On the academic side, we propose online algorithms with theoretical CRs for the problem described above. On the practical side, we investigate the real-world applicability of our methods and models on appointment-scheduling data from a partner health system. We develop new online primal-dual approaches for making not only a server-date allocation decision for each arriving customer but also an overtime decision for each server on each day within a horizon. We also derive a competitive analysis to prove a theoretical performance guarantee. Our online policies are (i) robust to future information, (ii) easy-to-implement and extremely efficient to compute, and (iii) admitting a theoretical CR. Comparing our online policy with the offline optimal policy, we obtain a CR which guarantees the worst-case performance of our online policy. We evaluate the performance of our online algorithms by using real appointment scheduling data from the UMHS. Our results show that the proposed online policies perform much better than their theoretical CR, and outperform the pervasive First-Come-First-Served (FCFS) and nested threshold policies (NTPO) by a large margin.

Analysis of unreliable BMAP/PH/N type queue with Markovian flow of breakdowns

Unreliability of components is the inherent feature of many real world systems and its account is vital for correct prediction of performance measures of the system. Multi-server queueing model considered in this paper allows to evaluate characteristics of the systems under much more general assumptions about the probabilistic distributions describing behavior of the system than models known in existing literature. We analyse the multi-server queue with infinite buffer and the Batch Markovian Arrival Process (BMAP) of customers. The servers are identical and independent of each other. Service time of a customer has phase-type (PH) distribution. Servers are subject to breakdowns and repairs. Breakdowns occurrence moments are defined by the Markovian Arrival Process (MAP). The breakdown causes a failure of any server, which is not under repair. When a server fails the repair period starts immediately. The duration of this period has PH distribution. A customer whose service is interrupted occupies an idle server, if any, and continues his/her service. If he/she does not see an idle server, the customer goes to the buffer with some probability and permanently leaves the system with the complementary probability. We derive the constructive ergodicity condition and calculate the stationary distribution and the main performance characteristics of the system. Illustrative numerical examples are presented.

Revenue Management of Reusable Resources with Advanced Reservations

We consider a revenue management problem wherein the seller is endowed with a single type resource with a finite capacity and the resource can be repeatedly used to serve customers. There are multiple classes of customers arriving according to a multi‐class Poisson process. Each customer, upon arrival, submits a service request that specifies his service start time and end time. Our model allows customer advanced reservation times and services times in each class to be arbitrarily distributed and correlated. Upon arrival of each customer, the seller must instantaneously decide whether to accept this customer's service request. A customer whose request is denied leaves the system. A customer whose request is accepted is allocated with a specific item of the resource at his service start time. The resource unit occupied by a customer becomes available to other customers after serving this customer. The seller aims to design an admission control policy that maximizes her expected long‐run average revenue. We propose a policy called the ε‐ perturbation class selection policy ( ε‐CSP), based on the optimal solution in the fluid setting wherein customers are infinitesimal and customer arrival processes are deterministic, under the restriction that the seller can utilize at most (1 − ε) of her capacity for any ε ∈ (0, 1). We prove that the ε‐CSP is near‐optimal. More precisely, we develop an upper bound of the performance loss of the ε‐CSP relative to the seller's optimal revenue, and show that it converges to zero with a square‐root convergence rate in the asymptotic regime wherein the arrival rates and the capacity grow up proportionally and the capacity buffer level ε decays to zero.

Non-parametric optimal service pricing: a simulation study

In this paper, we study a price discovery algorithm for searching the optimal price for a service with price-sensitive demand. The customer’s response to price is unknown and the customer arrival process follows an arbitrary point process. This algorithm is suitable for new services with no prior knowledge or historical data available. Furthermore, there is no information about objective function as well. We take on a simulation study and discuss the sensitivity and robustness of this procedure with respect to different arrival processes and customer response functions and also provide the comparative statics with simple price learning algorithm. We prove that price discovery algorithm is a better convergent as it reduces stochastic error at each step. The main focus of this research is to provide some guidance for the selection of sample sizes based on the test significance and the measure of its power when actual mean and variance for revenue are unknown.

Tightness of Stationary Distributions of a Flexible-Server System in the Halfin-Whitt Asymptotic Regime

A large-scale flexible service system with two large server pools and two types of customers is considered. Servers in pool 1 can only serve type 1 customers, while server in pool 2 are flexible – they can serve both types 1 and 2. (This is a so-called “N-system.”) The customer arrival processes are Poisson and customer service requirements are independent exponentially distributed. The service rate of a customer depends both on its type and the pool where it is served. A priority service discipline, where type 2 has priority in pool 2, and type 1 prefers pool 1, is considered. We consider the Halfin-Whitt asymptotic regime, where the arrival rate of customers and the number of servers in each pool increase to infinity in proportion to a scaling parameter n, while the overall system capacity exceeds its load by [Formula: see text]. For this system we prove tightness of diffusion-scaled stationary distributions. Our approach relies on a single common Lyapunov function G(n)(x), depending on parameter n and defined on the entire state space as a functional of the drift-based fluid limits (DFL). Specifically, [Formula: see text], where y(n)(·) is the DFL starting at x, and g(·) is a “distance” to the origin. (g(·) is same for all n). The key part of the analysis is the study of the (first and second) derivatives of the DFLs and function G(n)(x). The approach, as well as many parts of the analysis, are quite generic and may be of independent interest.

The impact of the $NT$-policy on the behaviour of a discrete-time queue with general service times

In this paper, we analyse the behaviour of a discrete-time single-server queueing system with general service times, equipped with the $NT$-policy. This is a threshold policy designed to reduce the number of service unit activation/deactivation cycles, whilst ensuring an acceptable delay trade-off. Once the server is deactivated, reactivation will be postponed until either $N$ customers have accumulated in the queue or the first customer has been in the queue for $T$ slots, whichever happens first. Due to this modus operandi, the system circulates between three phases: empty, accumulating and serving. We assume a Bernoulli arrival process of customers and independent and identically distributed service times. Using a probability generating functions approach, we obtain expressions for the steady-state distributions of the phase sojourn times, the cycle length, the system content and the customer delay. The influence of the threshold parameters $N$ and $T$ on the mean sojourn times and the expected delay is discussed by means of numerical examples.

An effective dynamic decision policy for the revenue management of an airline flight

Airline companies normally classify the seats of a cabin class into a number of fare classes. Customers of different fare classes arrive randomly during the booking horizon. Every time a customer in a certain fare class arrives, the airline company must decide promptly whether to fulfill or reject the request. To increase revenues, the airline company may reject certain lower-fare class customer requests and reserve the seats for future higher-fare class customers. However, rejecting too many lower-fare class customers may result in empty seats when the flight takes off. Given the multiple fare classes of a flight and the non-homogeneous Poisson customer arrival process in each fare class, and with the aim of maximizing the revenue of the flight, this study develops and tests two heuristic approaches – the dynamic seat rationing (DSR) decision policy and the expected revenue gap (ERG) decision policy – to help the airline make a fulfillment-or-rejection decision when a customer arrives. The simulation experiments show that ERG performs best among all tested approaches and, on average, the revenue from the ERG being merely 0.8% less than that of the optimal decision made with perfect information. Moreover, the ERG is very robust under various problem conditions.

Analysis of a versatile batch-service queueing model with correlation in the arrival process

In the past, many researchers have analyzed queueing models with batch service. In such models, the server typically postpones service until the number of present customers reaches a service threshold, whereupon service is initiated of a batch consisting of several customers. In addition, correlation in the customer arrival process has been studied for many different queueing models. However, correlated arrivals in batch-service models have attracted only modest attention. In this paper, we analyze a discrete-time D-BMAP/Gl,c/1 queue, whereby the service time of a batch is dependent on the number of customers within it. In addition, a timing mechanism is included, to avoid that customers suffer excessive waiting times because their service is postponed until the amount of customers reaches the service threshold. We deduce various useful performance measures related to the buffer content and we investigate the impact of the traffic parameters on the system performance through some numerical examples. We show that correlation merely has a small impact on the service threshold that minimizes the mean system content, and consequently, that the existing results of the corresponding independent system can be applied to determine a near-optimal service threshold policy, which is an important finding for practitioners. On the other hand, we demonstrate that for other purposes, such as performance evaluation and buffer management, correlation in the arrival process cannot be ignored, a conclusion that runs along the same lines as in queueing models without batch service.

예약기반 서비스 시스템에서의 고객 도착 프로세스 분석

Delivery of a good quality of service in an efficient manner requires matching the supply of capacity with customer demand. Much research has employed queueing models that analyzed the service system on the basis of independent and stationary customer arrivals. However, the appointment system, which is widely used to facilitate customer access to service in many industries including healthcare, has significant influence on the customer arrival process so that the independent and stationary assumption does not hold in an appointment-based service system. In this regard, this paper aims to propose a model for accurate illustration of the appointment-based customer arrival process. The use of the proposed model allows us to evaluate the overall system performance such as mean waiting time and service level under various appointment policies instead of conducting simulation studies.

System-Level Optimization in Wireless Networks: Managing Interference and Uncertainty via Robust Optimization

We consider a robust-optimization-driven system-level approach to interference management in a cellular broadband system operating in an interference-limited and highly dynamic regime. Here, base stations in neighboring cells (partially) coordinate their transmission schedules in an attempt to avoid simultaneous max-power transmission to their mutual cell edge. Limits on communication overhead and use of the backhaul require base station coordination to occur at a slower timescale than the customer arrival process. The central challenge is to properly structure coordination decisions at the slow timescale, as these subsequently restrict the actions of each base station until the next coordination period. Moreover, because coordination occurs at the slower timescale, the statistics of the arriving customers, e.g., the load, are typically only approximately known-thus, this coordination must be done with only approximate knowledge of statistics. We show that performance of existing approaches that assume exact knowledge of these statistics can degrade rapidly as the uncertainty in the arrival process increases. We show that a two-stage robust optimization framework is a natural way to model two-timescale decision problems. We provide tractable formulations for the base-station coordination problem and show that our formulation is robust to fluctuations (uncertainties) in the arriving load. This tolerance to load fluctuation also serves to reduce the need for frequent reoptimization across base stations, thus helping minimize the communication overhead required for system-level interference reduction. Our robust optimization formulations are flexible, allowing us to control the conservatism of the solution. Our simulations show that we can build in robustness without significant degradation of nominal performance.