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The California border inspection station discussed in the prior question, is considering the addition of a...

The California border inspection station discussed in the prior question, is considering the addition of a second inspector. The vehicles would wait in one lane and then be directed to the first available inspector. Arrival rates would remain the same (36 per hour) and the new inspector would process vehicles at the same rate as the first (40 per hour). a. What would be the average length of the waiting line? b. What would be the average time that a vehicle must wait to get through the system? c. What proportion of the time would the inspection station be empty? d. What is the average utilization of each inspector?

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Answer #1

This is a M/M/s queueing model, with number of servers, s = 2

Calculation of queue operating characteristics is following

a) Average length of waiting line (Lq) = 0.2285 (refer cell G13)

b) Average time in the system (W) = 0.0313 hours   (refer cell J13)

c) Proportion of time the insepction station would be empty (P0) = 0.3793   (refer cell E13)

d) Average utilization of each inspector (Rho)= 0.45   (refer cell F13)

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