Service Systems with Finite and Heterogeneous Customer Arrivals

Abstract

W e consider service systems with a finite number of customer arrivals, where customer interarrival times and service times are both stochastic and heterogeneous. Applications of such systems are numerous and include systems where arrivals are driven by events or service completions in serial processes as well as systems where servers are subject to learning or fatigue. Using an embedded Markov chain approach, we characterize the waiting time distribution for each customer, from which we obtain various performance measures of interest, including the expected waiting time of a specific customer, the expected waiting time of an arbitrary customer, and the expected completion time of all customers. We carry out extensive numerical experiments to examine the effect of heterogeneity in interarrival and service times. In particular, we examine cases where interarrival and service times increase with each subsequent arrival or service completion, decrease, increase and then decrease, or decrease and then increase. We derive several managerial insights and discuss implications for settings where such features can be induced. We validate the numerical results using a fluid approximation that yields closed-form expressions.

Please don't make me wait! Influence of customers' waiting preference and no‐show behavior on appointment systems

“…. Under this ES system, if all customers show up, the expected waiting time of each individual customer can Production and Operations Management be obtained following standard queueing approaches, such as the one in Section 3 of Wang et al (2014). There are two important features of the ES system that relate to our research.…”

“…Consequently, given specific values of N and T , we can reversely find a unique waiting time threshold θ, and the resultant appointment schedule is uniquely defined. The exact appointment time of any given customer $$n=1,\ldots,N$$ can be obtained using recursion (e.g., Section 3 of Wang et al., 2014). Next, we summarize three main features of the EW system that relate to our research.…”

“…Under this ES system, if all customers show up, the expected waiting time of each individual customer can be obtained following standard queueing approaches, such as the one in Section 3 of Wang et al. (2014). There are two important features of the ES system that relate to our research. Feature ES‐1 : Under the ES system, a later arrival expects a longer waiting time than an earlier arrival. Feature ES‐2 : Under the ES system, ceteris paribus , a customer prefers an earlier appointment to a later appointment. …”

Flexibly Serving A Finite Number of Heterogeneous Jobs in A Tandem System

“…We adopt a methodology similar to Wang et al. (2014). Let T m denote the time point when job m finishes service at station 1.…”

A Data-Driven Model of an Appointment-Generated Arrival Process at an Outpatient Clinic

“…Studies have found that no-show rates vary across different services and patient populations: the reported no-show rates are as low as 4.2% at a general practice outpatient clinic in the United Kingdom (Neal et al 2001) and as high as 31% at a family practice clinic in South Carolina (Moore et al 2001). Ever since the seminal papers of Bailey (Bailey 1952, Welch andBailey 1952), studies have analyzed queueing models that reflect key structural properties of appointment-generated arrival processes, e.g., see Kaandorp and Koole (2007), Hassin and Mendel (2008), Araman and Glynn (2012), Jouini and Benjaafar (2012), Feldman et al (2014), Honnappa et al (2015), Wang et al (2014), and Zacharias and Pinedo (2014).…”