Queuing Theory - 12 Single Server Model Calculating Utilisation Rate
#Operations Research - OR
#Operations Management - OM
#Queuing Theory
#Queuing Models
#Single Server Model
#Utilisation Rate
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Poisson - Exponential Single Server Model
Case:
On the help desk of an office of an insurance company, the arrivals of the customers follow the Poisson Law and, on an average, at every 10 minutes a customer arrive. The officer responsible takes, on an average, 6 minutes to serve a customer, assuming the service exponentially distributed.
Find the Utilisation Rate
Utilisation Rate = ρ = λ/μ (ρ = rho)
(i) Time unit of an hour (i.e. 60 minutes)
Utilisation Rate = ρ = λ/μ (ρ = rho)
= 6 / 10
= 0.6
(ii) for 15-minute interval
Utilisation Rate = ρ = λ/μ (ρ = rho)
= 1.5 / 2.5
= 0.6
(iii) 30-minute interval:
Utilisation Rate = ρ = λ/μ (ρ = rho)
= 3 / 5
= 0.6
Thus, if we change the magnitude of the time unit, the utilisation rate remains the same. i.e. its magnitude doesn't change.
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