Question

Two hot dog vendors at a football game get a surge of customers arriving as a Poisson Process with rate 10 per minute during halftime. Each vendor takes half a minute on average to serve one customer. The waiting line has space for the one or two customers being served plus 15 more to wait. If more than 15 are waiting, the line starts to obstruct foot traffic.

Estimate the number of minutes until foot traffic is obstructed, if the line is empty at the start of halftime.

Suppose it takes a vendor an exponentially distributed number of minutes to serve one cus-tomer, with parameter 2 (half a minute on average). Define variables and write equations for the expected number of minutes until the line starts to obstruct foot traffic.

Answer 1