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Unformatted text preview: UNIVERSITY OF SOUTHERN CALIFORNIA, FALL 2008 1 EE 550: Problem Set # 7 Due: Wednesday, November 12, 2008 I. SLOTTED TIME AND PERIODIC SERVICE OPPORTUNITIES Consider a packet transmission system that operates in slotted time with fixed slot size T . Packets arrive according to a Poisson process of rate λ , and all packets have fixed size with service time T . However, service opportunities arise only once every M slots. Specifically, the first service opportunity arises at time and has duration T . The transmitter is then idle during time [ T,MT ) , and has its second service opportunity at time MT , its third service opportunity at time 2 MT , etc. Only a single packet can be served during a service opportunity, and it can only be served if it arrives before the opportunity starts. For example, if the first packet arrival of the system arrives at time MT- . 2 T , then it arrives to an empty system and its full waiting time in the system (including queueing and service) is equal to (1 . 2) T . Compute the exact average delay W in the system (including queueing and service). What is the maximum rate λ under which the system is stable (with finite W )? Hint: Define “frame k ” as the interval of size MT that starts at the k th service opportunity. Regard each packet service as having an “effective” service time of MT , but make sure to appropriately account for any residual times in the system. II. COMPARISON OF MULTI-ACCESS PROTOCOLS IN A N-USER SYSTEM Consider a slotted multi-access system with unit slot sizes that begin on slot boundary times t ∈ { , 1 , 2 , 3 ,... } . There are N users in the system. Suppose the arrival processes are independent and Poisson with rate λ i , for each user i ∈ { 1 ,...,N } . All packets are the same size and have transmission time of one slot. All users want to transmit to the same wireless access point. Consider the following three different multi-access protocols: 1) Periodic Round Robin Service : Service Opportunities for user i arise every N slots, at slots t such that ( t mod N )+1 = i ....
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This note was uploaded on 12/21/2010 for the course EE 550 taught by Professor Neely during the Fall '08 term at USC.

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