Consider the following process. Arriving orders are split into two jobs, which go through different paths. One job is processed by the top path that consists of three steps (A, B, and C), while the other is processed in parallel by the bottom path, consisting of a single step (D). The two jobs rejoin following processing and the order is considered complete. Each circle in the diagram represents a single server, and the times indicate average processing times, in minutes.

First assume, there is no variability in either inter-arrival times or processing times, and throughput is less than system capacity, then

(a) [1] What is capacity of the system (in orders/hr)?

(b) [1] Which path is critical? What is its length (in minutes)?

Now assume that the time between individual job arrivals is exponentially distributed and orders arrive at the rate of 5 orders/hr. Further, assume that all service times are exponentially distributed.

(c) [2] Which path is critical? What is its length (in minutes)?

(d) [1] In this new system, does the bottleneck lie on the critical path? Write either YES or NO (only one answer applies).

(A) 3 min (B) 4 min 6 min AND (D) 10 min