Question

. An immigration agent at an airport, on an average, could process 15 entrants in one hour, if he was busy all the time. On an average, an entrant arrives at his station at every 5 minutes. The current agent can be replaced by a more efficient specialist. The specialist can process 18 entrants in one hour. The specialist is paid $30 per hour whereas the current agent is paid $25 per hour. An entrant’s time is considered to be worth $10 per hour. Calculate the total cost of paying the current agent and the entrants’ time in the system and the total cost of paying the specialist and the entrants’ time in the system to decide whether to replace the current agent with the specialist.

Answer 1

1. Current agent

This is a M/M/1 queue system with following parameters

Arrival rate, $\lambda$ = 60/5 = 12 per hour

Service rate, $\mu$ = 15 per hour

Service cost, Cs = $ 25 per hour

Cost of entrants time in the system, Cw = $ 10 per hour

Average number of entrants in system, L = $\lambda$/($\mu$-$\lambda$) = 12/(15-12) = 4

Total cost of paying the current agent and entrants time in the system = L*Cw + Cs

= 4*10+25

= $ 65 per hour

2. Specialist

This is a M/M/1 queue system with following parameters

Arrival rate, $\lambda$ = 60/5 = 12 per hour

Service rate, $\mu$ = 18 per hour

Service cost, Cs = $ 305 per hour

Cost of entrants time in the system, Cw = $ 10 per hour

Average number of entrants in system, L = $\lambda$/($\mu$-$\lambda$) = 12/(18-12) = 2

Total cost of paying the specialist and entrants time in the system = L*Cw + Cs

= 2*10+30

= $ 50 per hour

Total cost of paying the specialist and entrants time in the system is lower.

Therefore, current agent should be replaced with the specialist.