Question

Please fill in all question marks!!!!

Problem 15-25 (Algorithmic)

Burger Dome sells hamburgers, cheeseburgers, French fries, soft drinks, and milk shakes, as well as a limited number of specialty items and dessert selections. Although Burger Dome would like to serve each customer immediately, at times more customers arrive than can be handled by the Burger Dome food service staff. Thus, customers wait in line to place and receive their orders. Suppose that Burger Dome analyzed data on customer arrivals and concluded that the arrival rate is 27 customers per hour and 1 customer processed per minute.

Compare a multiple-server waiting line system with a shared queue to a multiple-server waiting line system with a dedicated queue for each server. Suppose Burger Dome establishes two servers but arranges the restaurant layout so that an arriving customer must decide which server's queue to join. Assume that this system equally splits the customer arrivals so that each server sees half of the customers. How does this system compare with the two-server waiting line system with a shared queue? Compare the average number of customers waiting, average number of customers in the system, average waiting time, and average time in the system. If required, round your answers to four decimal places.

	Shared single queue	Dedicated queues
Number of customers waiting	??????	???????
Average number of customers in the system	??????	????????
Average waiting time	?????minutes	???????minutes
Average time in the system	???????minutes	????????minutes

2. Comparing these numbers, it is clear that the???????? results in better process performance than the??????? .

Answer 1

ANSWER:

Given that,

This is a single queue channel

The number of customers per hour is =27

1 customer processed per minute.

Mean number of arrivals per time period is

λ=27/60 = 0.45

the mean number of service time period

  ρ=λ/µ = 0.45/1 = 0.45

a)

The number of customers waiting is =

L_q=λ²/ µ(µ-λ)

= 0.45²/ 1(1-0.45)

=0.2025/0.55 =0.37

L_q=0.37

b)

Average number of customers in the system

N_c=L_{q +} λ/µ

=0.37 + 0.45/1

=0.37+0.45 = 0.82

N_c=0.82

c)

Average waiting time

A_T= L_q / λ

=0.37/0.45

A_T =0.82

d)

Average time in the system is

A_TS = A_T+ 1/µ

=0.82+ 1/1

=0.82+ 1

A_TS  = 1.82