Queueing system with exponential arrival, service

[bjr_jyd15]

I'm having troubles with the basics here--do I use exponential process or poisson?

Suppose a queueing station has two servers, an exponential inter-arrival time for customers with a mean of 2 hours and an exponential service time for service with mean of 2 hours. Furthermore a customer has just arrived at 12 noon.

1. What is the probability that the next arrival will be before 1:45pm?

I have tried using exponential distribution with lambda = 0.5...but can't figure out what I'm doing wrong.

Thanks.

 

[lippyka]

The probability that the next arrival will be before 1:45pm can be calculated using the exponential distribution. The probability is given by the equation: P(x<1.45) = 1 - e^(-lambda*x), where lambda = 0.5 and x = 1.75 (1.45pm - 12 noon). Therefore, the probability of the next arrival being before 1:45pm is 0.38292492.