Cooperative Hypercube Queuing Model for Emergency Service Systems

Han Liu,Hao Yin,Yang Zhou,Meng Li

doi:10.1155/2021/6653573

Abstract

As a useful descriptive tool for emergency service effectiveness, the hypercube queuing model has been applied in systems of many countries, such as the SAMU system in Brazil. However, the traditional hypercube queuing model and its extended forms assume that the service provider performs independent services, lacking a compelling description of the situation where emergency vehicles perform cooperative services (e.g., NEPPHE in China). To this end, we assume that vehicles in the same fleet simultaneously start and end services and propose a cooperative hypercube queuing (CHQ) model that can describe the state of emergency systems which apply multivehicle dispatches. In order to verify the accuracy of the model, we apply Arena simulation software in Wuhan case. The results show that the CHQ model can illustrate cooperative performance effectively. Sensitivity analyses under more general parameters are conducted to reveal insights into the model application.

Highlights

In recent decades, deterministic and probabilistic models on the emergency facility location have been studied. e location set covering problem (LSCP) model by Toregas et al [7] and the maximum coverage location problem (MCLP) introduced by Church and ReVelle [8] are two classic models that regard the emergency system as static and deterministic
Gendreau et al considered the characteristics of different coverage radii of various facilities and proposed the dualstandard coverage model (DSM) [12]. e optimization result of facility locations ensures that at least a certain percentage of demand points are located within the smaller standard radius while locating all demand points within the larger standard radius
We propose the cooperative hypercube queuing model by assuming that certain types of calls require cooperative service; cooperative servers can become free simultaneously from busy states

Summary

A A or B A or B or C

—— V3 — V3 V1 servers (V2 and V1) are simultaneously dispatched; if any one of the two servers is busy, the third one (V3) would be dispatched as a backup one; if any two servers of the three candidates are both busy, the only idle one would be dispatched as a single dispatch. (ii) A medium-risk call requires the dispatched fleet, including servers of two types (an ambulance and a police car together). When a medium-risk call arrives, the fleet composed of the nearest ambulance and a police car will serve as the first preferred fleet; if either one is busy, a further available server of the absent type would be selected to formulate the second preference fleet; otherwise, the call is lost to other systems. (iii) A high-risk call requires cooperative servers of three types (an ambulance, a police car, and a fire engine). Calls of this type respond to the highest-level severity. A new extension of the classic hypercube model is proposed

CHQ Model and Validation

Sensitivity Analysis

Findings

Conclusions