Messages arrive at a switching center in accordance with a Poisson process havin
ID: 3152765 • Letter: M
Question
Messages arrive at a switching center in accordance with a Poisson process having mean arrival rate of 180 messages/hr. They are then sent over a transmission line at the rate of 12 characters per second. The length of the messages is exponentially distributed with a mean of 144 characters. 1) What is the mean waiting time at the switching center? 2) What will be the mean number of messages waiting for transmission? 3) What is the probability that a message does not have to wait to be transmitted?
Explanation / Answer
Mean number of characters per message = 144
Mean arrival rate = 180 messages per hour
Mean Service Time = 1/12 messages per second
= 1/12 * 3600 = 300 per hour
= 180 ; = 300
1.) Lq = 2 / ( - )
= 0.9
Wq = Lq /
= 0.9/7.2
= 0.005 hours
W = W + 1/
= 0.005 + 0.0033
= 0.00833 hours
Mean waiting time at the switching center = 0.00833 hours = 30 seconds
2.) Number of messages waiting for transmission = Lq = 0.9 messages
3.) The probability that an arriving unit has to wait for service = Pw = /
= 0.6
The probability that a message does not have to wait to be transmitted = 1 - 0.6 = 0.4