A service station has one gasoline pump. Cars wanting gas arrive according to a Poisson process at a mean rate of 20/hour. However, if the pump is in use, these potential customers may balk (refuse to join the queue). To be more precise, if there are n cars already at the service station, the probability that an arriving potential customer will balk is n/4 for n = 1, 2, 3, 4. The time required to serve a car has an exponential distribution with a mean service time of 3 minutes.

(a) Construct the transition rate diagram for this system.

(b) For all k, find the differential-difference equations for pk (t) = Prob{k in system at time t}.

(c) Determine the stationary probability distribution and hence find the average number of cars at the station.

 

Alpha Geek

(8)

Status NEW Posted 06 Jun 2017 02:06 PM My Price 5.00

-----------

Attachments

1496760942-1909298_1_636322638745925692_media-f0a-f0a885fd-0040-453d-bd3b-5f6666ca8a34-phpHJTYSx.png

1496760943-1909298_2_636322638745925692_media-db0-db0eea54-8cee-4e31-8f89-ceb87825fc79-phpw3cULa.png

1496760945-1909298_3_636322638745925692_media-13d-13d767b9-2ffd-40e2-98e2-04730d5885fe-phprTFHDQ.png

Not Rated(0)

• Buy Answer