Hospital Simulation

Problem Brief

ABC NHS Trust provides medical services for around half a million people. The focus here is on inpatient, non- emergency services such as surgery for a given medical specialty.

The Department of Health has defined the Referral to Treatment Time (RTT) as a key performance measure; this is the time from a patient's referral to the start of treatment. Each patient arrives at ABC having already waited (the time since referral) a time called Elasped Time Since Referral (ETSR). Only the ABC system will be the time from arrival at ABC to treatment at ABC, a patient's RTT = ETSR + W.

Patients are classified as either urgent (U) or routine (R). Inter-arrival times are assumed to be independent and exponentially distributed. The rate of arrivals, per day is 3.69 for urgent and 2.19 for routine. Recall that the mean inter-arrival time is the time it takes (on average) for one arrival, and is the inverse of the arrival rate (the number of arrivals per unit time, on average). Service (treatment) times are constant (fixed) and equal to 1/6 days.

ETSR is modelled as follows: for R patients, it has a Normal Distribution with mean 70 days and standard Deviation 15 days (negative samples may be reset to zero; for simplicity this is not required); for U patients it has an Exponential Distribution with mean 50 days. Services is given according to the following priority rule:

• U patients have priority over R ones
• Within each type (U, R) priority is given to those with higher ETSR

This priority rule is complete (ties are virtually impossible): since both ETSR distributions are continuous, the probability that any two patients have the same ETSR is zero. We aim for a basic simulation in which patients are treated as Simul8's generic items (patients' appointments are not modelled). Output of interests are: (1) The fraction of patients whose RTT is no more than 18 weeks, (2) The effect of the priority rule on average waiting times. Specifically for each case, U and R, let x denote the ETSR as follows: x \(\leq\) F-1 (1/3) is small (S); x > F-1 (2/3) is large (L); otherwise it is medium (M). We want to estimate the mean waiting time at ABC (the W above) for each of the six categories formed by the patient types (U, R) and ETSR categories (S, M, L).

These outputs refer to long-run behaviour (steady state), but early parts of a simulation tend to depend heavily on the choice of initial system state (that is, at time zero). Thus: assume the initial system state is "empty"; use a warm-up of 200 days; and exclude the data observed during the warm-up. For consistency, all times should be measured in days.