Question

At a physician's office, patients sit in the Waiting Room until it is their turn (first-come, first-served) to be seen by the doctor. There is only one doctor on duty, and the doctor can help only one patient at a time. Based on her long-run rate of client service, this doctor typically spends 30 minutes per patient. Whenever the doctor finishes her session with one patient, she immediately begins a new session with the next patient.

When you arrive in the Waiting Room, the doctor has just begun her session with a patient, and you see that there are 4 other patients already waiting.

In this situation, it is reasonable to model your time (hours) in the Waiting Room as an Erlang random variable with:

λ=?

w=?

Answer 1

From the given information, patients sit in the waiting room until it is their turn on First- come First serve basis. There is only one doctor on duty and the doctor can help only one patient at a time, which means it is M/M/1model. Given that, when a new patient arrives to the waiting room there are four other patients already waiting in the room. 60 If the customers arrive according to the Poisson process then the mean arrival rate, 1 = 1 The time taken to treat a patient which means service rate d= ~= 2 That is, Then the waiting time of the distribution is W =W,+= Here w. -1 and 1,- Ft Number in the Queue is calculated as 0.52 1-0.5 = 0.5

Wait in the Queue is calculated as Then the waiting in the system is calculated as W =W +- - = 0.5 + 1 / 2 = 0.5+0.5 = 1 Therefore, waiting in the system is one hour if the arrival times and the services time are exponentially distributed. As the distribution of mean arrival rate and the service rates are not given it is not possible to calculate Erlang random variable with parameter 2 and W