Question

restaurant is planning to add a bar – the bar can have only six barstools. Customers interested in having a drink at this bar arrive at a rate of 6 per hour following a Poisson distribution. It is expected that a customer stays 30 minutes, exponentially distributed. There are only 3 spaces available for customers to wait for a barstool to become available. Customers who want to come in and find there is no room to wait, go to the restaurant next door. Determine:
A. Probability that there are no customers at the bar.
B. The probability that an arriving customer has to wait for a barstool.
C. The average number of customers at the bar.
D. The average number of customers waiting.

Answer 1

Customers arrival rate can be termed as = 6 = 6 customer per hour

Capacity to serve the in the hour = 30 minutes for 1 customer= 2 customers in hour that is termed as    and 6 chairs means 6 parallel services at a time which is termed as c

A) We need to find the probability that there is no customer in the bar

WE have which is called the utilization of the server or the probability that the server is busy

We have = 6/2x6=1/2

We have P0 means there is no customer that means Probability of the servers are not busy

P0={ !+} (hints the denominator is n!, and the whole to the power -1)

which is equal to ++++++The whole to the power -1

=1+3+4.5+4.5+3.375+2.025+2.025=(20.8)=0.0480

B) the probabiility of customer waiting means

Probability of There are 6 customer in the systems

Pro 6 customers in the system at a given point = =(3^6/6!)0.0480=0.0486

D)

Average number of customers waiting = LQ= =.0480x729x.5/720x.25=.0972