Find probability of no units in the system

Assignment Help Operation Management

Reference no: EM13227299

1. In a waiting line situation, arrivals occur at a rate of 2 per minute, and the service times average 18 seconds. Assume the Poisson and exponential distributions.

a. What is l? - Average number of arrivals expected during some time period

b. What is m? - Average number that the system can serve during some time period

c. Find probability of no units in the system.

1-λ/ µ = 1 - 2/18=0.89

d. Find average number of units in the system.

Ls = λ/( µ- λ) = 2/(18-2) = 0.125

e. Find average time in the waiting line.

Wq= λ/ µ( µ- λ) = 2/18(18-2) = 0.006

f. Find average time in the system.

Ws= 1/ (µ- λ)= 1/(18-2) = 0.0625

g. Find probability that there is one person waiting.

(λ/ µ) = 2/18 = 0.11

h. Find probability an arrival will have to wait.

2/18(18-2) = 0.006

2. The Sea View Resort uses a multiple-channel queue registration system. If the average service time is 8 minutes, there are three registration clerks, and guests arrive at the rate of one every 5 minutes, find

a. l and m.

l 60/5=12 m= 60/8 = 7.5 customers/hr

b. the probability all three clerks are idle.

(THE PROBABILITY OF NO UNITS IN THE SYSTEM) 1/[(12/7.5)^0/0!+(12/7.5)^1/1!+ (12/7.5)^3/3!(1/1-12/3(7.5)]

P0 = .1872

c. the probability a guest will have to wait.

(PROBABILITY THAT AN ARRIVING UNIT HAS TO WAIT)

Pw = .2738

d. the average time a customer is in line.

Wq= Lq/l = .0261

e. the average number of customers in line.

Lq = 0.3129

3. The post office uses a multiple channel queue, where customers wait in a single line for the first available window. If the average service time is 1 minute and the arrival rate is 7 customers every five minutes, find, when two service windows are open,

a. the probability both windows are idle.

Po = .1765

b. the probability a customer will have to wait.

Pw = .5765

c. the average time a customer is in line.

Wq = .1922

d. the average time a customer is in the post office.

W= .3922

Reference no: EM13227299

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