Question

Dr. Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can shoot a dog every 4 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 5 minutes according to a Poisson distribution. Also assume that Taruna's shooting times are exponentially distributed.Compute the following:a) The probability that Tarun is idle.b) The proportion of the time that Tarun is busy.c) The average number of dogs being vaccinated and waiting to be vaccinated.d) The average number of dogs waiting to be vaccinated.e) The average time a dog waits before getting vaccinated.f) The average amount of time a dog spends waiting in line and being vaccinated.

Answer 1

Check the following explanation and images attached

Step-by-step explanation:

The assumptions in single-server queue theory include: -

Unlimited calling population may enter the queue

Arrivals are random and independent but average number of arrival does not change.

Single waiting line and arriving customers are patient customers who can wait in the queue before they can be served regardless of the length of the line.

Arrivals are served on FIFO basis

Service time of one customer may vary from that of another customer.

Single server and service time is as per the negative exponential probability distribution.

Average service rate is greater than average arrival rate.