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?
