question archive Supermarket X has two entrances on opposite sides of the streets (queues are independent)

Supermarket X has two entrances on opposite sides of the streets (queues are independent)

Subject:Operations ManagementPrice: Bought3

Supermarket X has two entrances on opposite sides of the streets (queues are independent). There

is one server who sells ticket at each of these entrances. The arrival rate to each of the queues is

the same and is equal to 8 customers per hour. One server is faster than the other one. Service

time for server A is 4 minutes on average for each customer while server B can serve on average

20 customers per hour. Assume all the inter-arrival times and service times are exponentially

distributed.

i). On average, how many customers are waiting (not including those receiving service) in

Supermarket A?

ii). The boss of Supermarket A is considering closing down the slower server. Assume that in this

case the faster server would serve all 16 arrivals per hour and the service rate does not change

(the inter-arrival times and service times are still exponentially distributed). To choose between

these options, the boss needs to do cost analysis. Assume that the boss has estimated

that waiting in line is costly in terms of dis-utility of customers and each customer incurs $10

cost in an hour wait in the line. On the other hand, the boss pays $7 to each server. Can you help the boss to make decision under this situation?

 

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