  This work develops a methodology for studying the effect of an offload zone
on the ambulance ramping problem using a multi-server, multi-class
non-preemptive priority queueing model that can be treated analytically. A
prototype model for the ambulance/emergency-department interface is
constructed, which is then implemented as a formal discrete event simulation,
and is run as a regenerative steady-state simulation for empirical estimation
of the ambulance queue-length and waiting-time distributions. The model is also
solved by analytical means for explicit and exact representations of these
distributions, which are subsequently tested against simulation results. A
number of measures of performance is extracted, including the mean and 90th
percentiles of the ambulance queue length and waiting time, as well as the
average number of ambulance days lost per month due to offload delay (offload
delay rate). Various easily computable approximations are proposed and tested.
In particular, a closed-form, purely algebraic expression that approximates the
dependence of the offload delay rate on the capacity of the offload zone is
proposed. It can be evaluated directly from model input parameters and is found
to be, for all practical purposes, indistinguishable from the exact result.
