Consider a server where packets arrive according to a Poisson stream with a rate of 4 packets per minute. Half of the packets have a processing time of exactly 10 seconds (Type 1), a quarter of the packets have a processing time of exactly 15 seconds (Type 2) and the remaining quarter have a processing time of 20 seconds (Type 3). The packets are processed in order of arrival.

(a) Determine the mean sojourn time (waiting time plus processing time) of a type 1, 2 and 3 packets and also of an arbitrary packet.

One decides to process smaller packets with priority. So type 1 orders have highest priority, type 2 orders second highest priority and type 3 orders lowest priority. Determine the mean sojourn time of each type of packets and an arbitrary packet if: (b) Packets processed at the server may not be interrupted. (c) Type 1 and type 2 packets may interrupt the processing of a type 3 packet. Type 1 packets may not interrupt the processing of a type 2 packet.