Service Capacity Reserve under Uncertainty by Hospital’s ER Analogies: A Practical Model for Car Services

Table 2

Queuing system steady-state measures of effectiveness.

Steady-state measures of effectiveness	Variable	Name
Nveh=TVWDM	Number of vehicles arriving to the service	Nveh
Simulation variable	Average number of vehicles in the Q-NTec	𝐿
Simulation variable	Average number of vehicles in the Queue	Lq
FTI=1−WtecxNTec=𝑃0+𝑠−1𝑠×𝑃11+⋯+𝑠×𝑃𝑆−1	Fraction of time that a technician is idle	FTI
VhW=NVeh−𝐿	Average number of vehicles that are being worked	VhW
Wtec=𝐿−Lq=NTec−∑^𝑠−1𝑛=0(𝑠−𝑛)∗𝑃𝑛	Average number of technicians that are working	Wtec
EFCTec = VhWNVeh	Operating efficiency per vehicle	EFCVeh
EFCVeh=WtecNVeh	Operating efficiency per technician	EFCTec
1𝜇=TSW×60	Service rate [vehicles/hour]	𝜇
1𝜆=TSR×60	Arrival rate [vehicles/hour]	𝜆
𝑃𝑛=NVeh!×𝜆ℎ!×(NVeh−ℎ)!𝜇^ℎ×𝑃0	Probability 𝑛 vehicles are in the queuing system (Q-Ntec)	Pn
𝑃𝑛=1(𝑃0)^−1	Probability of no calling units in the queuing system.	Po
Initial Po_inverse = 0, then: 𝑃0=(𝑃0)^−1+den_1	Po inverse	Po^−1
f(den_1)=NVeh!×𝜆ℎ!×(NVeh−ℎ)!𝜇^ℎ	Operator	f(den_1)