Technical Note—Approximating Vehicle Dispatch Probabilities for Emergency Service Systems with Location-Specific Service Times and Multiple Units per Location

Abstract

To calculate many of the important performance measures for an emergency response system one requires knowledge of the probability that a particular server will respond to an incoming call at a particular location. Estimating these "dispatch probabilities" is complicated by four important characteristics of emergency service systems. We discuss these characteristics and extend previous approximation methods for calculating dispatch probabilities, to account for the possibilities of workload variation by station, multiple vehicles per station, call and station dependent service times, and server cooperation and dependence.

Ambulance location for maximum survival

“…The authors propose the following iterative heuristic: 1) Initialize the vector 1 p of busy probabilities to an estimated system-wide busy probability To compute the busy probabilities, the authors generalize (Budge at al, 2007a) and employ an approximation scheme based on the well known hypercube queuing model of Larson (1974Larson ( , 1975. A detail about the busy probabilities requires attention: The busy probability associated with an EMS station with no allocated EMS units is 1 (and not 0).…”

Hypercube Queuing Models in Emergency Service Systems: A State-of-the-Art Review

“…There are three main ways to evaluate the performance of a system [13]: 1) exact approaches (e.g., HQM proposed by Larson [12]), 2) discrete-event simulation, and 3) approximate approaches (e.g., approximate hypercube (AH) model proposed by Larson [14]). The advantages of the approximate procedures in comparison with two other ones are that their computation time is low and is not influenced by the features of the system.…”

“…Also, we have: As mentioned before, the objective function (12) maximizes the expected number of demands that are covered. Constraint (13) calculates how many times demand point is covered. Constraint (14) limits the maximum number of facilities that can be deployed, and Constraint (15) shows that more than one server can be assigned to each facility.…”

“…Budge et al [13] proposed an approximation algorithm based on the Jarvis' algorithm, in which more than one server can be assigned to each station; therefore, they computed a station (instead of server) busy probability. Also, in this algorithm, a set of correction factors is formulated based on random sampling of stations.…”

Scheduling ambulance crews for maximum coverage

“…We use a version of the AH model from Budge et al (2008) that allows for the possibility of multiple ambulances per station to directly compute the expected coverage s(.) for a given solution, instead of using the approximation in (4).…”