Delay Distributions in Appointment Systems with Generally and Non-Identically Distributed Service Times and No-Shows

Assessing appointment systems’ operational performance with policy targets

“…This is consistent with Bailey's (1952) observation based on simulation and an analytical proof in Millhiser and Valenti (2012) for IBFI schedules with Markovian service times and no no-shows. Likewise, we are unable to find any counterexample to the monotonic deterioration of waiting in IBFI schedules for any service time mean, c.v., show rate, or fixed-interval size.…”

“…To assess targets (i) and (ii), we employ the stochastic model of Millhiser and Valenti (2012) which gives the cumulative probabilities of individual patient waits and doctor overtime in any appointment template with generally and non-identically distributed service times and no-shows. This allows us to answer the research questions posed above by solving a problem computationally that simulation studies have only partly addressed.…”

“…This section summarizes the Millhiser and Valenti (2012) stochastic model and demonstrates it with a numerical example. The basic premise is that delay distributions are predicated on the actual progress of the doctor's busy periods in the session, where a busy period is the duration of continuous consultations between successive doctor idle times.…”

“…Patient n will show, punctually, with probability α n (0 ≤ α n ≤ 1) and our experiments employ the special case α 1 = α 2 = · · · = α N . Millhiser and Valenti (2012) derive the probability that patient n − 1 finishes service at most t time units after time d n as W n (t), n = 1, . .…”

“…representing an infinitesimally short service time if patient i is a no-show. The definition of W n (·) is also modified to account for the probabilities that each patient will not show (for details, see Millhiser and Valenti, 2012, Section 2.2). To illustrate, consider N = 2 patients who arrive at minutes d 1 = 0 and d 2 = 15 with session end time d 3 = 30.…”