Question

An airline ticket office has two ticket agents answering incoming phone calls for flight reservations. In addition, one caller can be put on "hold" until one of the agents is available to take the call. If all three phone lines (both agent lines and the hold lines) are busy, a potential customer gets a busy signal, and it is assumed she calls another ticket office, so that her business is lost. The calls and attempted calls occur randomly i.e., according to a Poisson process) at a mean rate of 12 per hour. The length of a telephone conversation has an exponential distribution with a mean of 4 minutes a) Construct the rate diagram for this queuing system. b) Find the steady state probability that i. A caller gets to talk to an agent immediately ii. The caller is put on hold iii. The caller gets a busy signal

Answer 1

Answer * According to collect from the data * let us assume that the equations are in - * the call and attempted cally occurs randomly the rate of 12 hours t it is the lingth of telephone conversation has exponential distruction with the mean of Minuty * To Construct the rate of diagram for the queing system @ to findout the let d=12 per hour. steady state probability all ll= 6014 = 15 per hour $52, k-S1 and k=3 - To calculate the queue characterstics of follows

M/M/s Finite Queue Model Expected number of customers lost due to balking = 0.6833 Data 12 15 2 3 (mean arrival rate) (mean service rate) (# servers) (max customers) Results L = 0.8114 La = 0.0569 W = 0.0717 W, = 0.0050 p=0.4000 0.5000 0.4500 0.4000+ 0.3500 0.3000 La 0.2500 20.2000 0.1500 0.1000 0.0500 HT 105 6 '' 12' 15' 18 '21' 24 Number of Customers in System n Po 0 0.4448 0.3559 0.1423 3 0.0569 0.0000 0.0000 0.0000 0.0000 0.0000 9 0.0000 10 0.0000 11 0.0000 12 0.0000 13 0.0000 14 0.0000 15 0.0000 0.8000 0.3200 0.1280 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.3559 0.2847 0.1708 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0569 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

1. agent immediately are 3 ) They are callers to get talk to an * Po+P = 0.44848 +0.3559. e . ) 0.8007 (ii) it is the caller put on hold > I-COPPA) = 1-0.8007 - 0.1993 (i) The calley of get busy of Signal - P3 = 0.0569