Sep 19, 2017

# PRINTED CIRCUIT BOARDS ARRIVE AT A COMPONENT INSERTION FACILITY ACCORDING TO A POISSON…

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Printed circuit boards arrive at a component insertion facility according to a Poisson distribution at a rate of one every 6 seconds. The number of components to be inserted onto a board has a geometric distribution with parameter p = 0.5. The time to insert each component is a constant τ seconds.

(a) Compute the mean, second moment, and variance of the time required to insert the components onto an arbitrary printed circuit board.

(b) Assuming that the printed circuit boards are serviced in first-come, first-served order, find the mean time spent by an arbitrary circuit board at the insertion facility.

(c) Now assume that the servicing of printed circuit boards requiring the insertion of only one component (called type-1 circuit boards) are given non preemptive priority over the servicing of all other circuit boards (called type-2 circuit boards). Compute the mean response time of type-1 and type-2 circuit boards in this case.

(d) Given that τ = 2, find the mean response time of an arbitrary printed circuit board under the non-preemptive priority scheduling of part (c) and compute the relative improvement over the FCFS order.

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