{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hmwk10sol+_2_

# hmwk10sol+_2_ - ISyE 3232 Stochastic Manufacturing and...

This preview shows pages 1–2. Sign up to view the full content.

ISyE 3232 Stochastic Manufacturing and Service Systems Fall 2011 H. Ayhan Solutions to Homework 10 1. Let S 1 and S 2 be independent and exponentially distributed random variables with means 1 μ 1 = 3 and 1 μ 2 = 6. They corresponds to the service time of the first and the second teller. (a) Since A starts service immediately after arrival, P ( T A 6) = P ( S 1 6) = e - 1 2 × 6 = 0 . 0498. (b) By the same reason, E ( T A ) = E ( S 1 ) = 3. (c) This amount, in mathematical expression, will be E ( T A | T A > 6) = E ( S 1 | S 1 > 6) = 6 + E ( S 1 ) // by memoryless property of exponential random variables = 9 . (d) P ( T A < T B ) = P ( S 1 < S 2 ) = μ 1 μ 1 + μ 2 = 2 / 3 . (e) The time from noon till a customer leaves is min { T A , T B } . Its expectation will be the same as E (min { S 1 , S 2 } ) = 1 μ 1 + μ 2 = 2 . (f) If a customer leaves, one of the tellers will be able to serve C . So it is the same as time till one departure, which is computed in (e). (g) The total time C spends in the system will be the summation of the waiting time min { T A , T B } and its service time. The service time will depend on at which teller the

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

hmwk10sol+_2_ - ISyE 3232 Stochastic Manufacturing and...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online