ECEN4533      Final Exam    2 May 2007

1) An ATM switch connected to a 310 Kbps output trunk line is fed 430 byte packets, on average.  The packet size and packet inter-arrival time (IAT) are known to be exponentially distributed.  The ATM switch takes the packets and chops them up into fixed size cells via AAL5.  The average cell time in the system is desired to be < 92 msec.
1a [10] Compute the maximum load, ρ, that can be placed on this system assuming an M/D/1 queue. [Answer: 0.9927]
1b [10] Given the load from 1a, compute the packet IAT.  [12.40 msec]
1c [10] Compute the Carrying Capacity of this ATM system.  [0.7971]
1d [10] Given that the packet IAT's are exponentially distributed and that these packets are chopped into cells at the input card of an ATM switch, is the choice of modeling the ATM switch as an M/D/1 queue a good one?  Explain.  [No.  The "D" portion is correct since the cells are fixed size, but the cells are probably not arriving at the output port in an exponentially distributed manner.  Per the problem statement the packets are arriving with an exponential distribution, but once chopped into cells, the cells are likely arriving in periodic clumps.]

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2) Ninety-one 780 Kbps input lines are connected to a packet switch.  Each input line has a 39% load.  Hence there are 27.68 Mbps entering this switch, on average.  The switch is connected to a 43 Mbps output trunk.
[30] Compute the probability that, at any instant in time, the instantaneous bits/second entering the switch exceeds the output line speed.  [8.54*10-6, which comes out to about 4.49 minutes every year.]
[5] If traffic is entering the switch at 7.8 Mbps, a value less than the output line speed, will there be any packets in a switch queue?  Explain, based on your understanding of the internal workings of a typical switch.  [There may be packets in the queue.  If > 2 or more packets simultaneously arrive, only one can be output and others must be temporarily stored.]

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3) A corporate voice system is using an 11 Kbps fixed rate voice coder built into stand-alone VoIP phones.  In each phone, the voice coder is followed by a packet assembler which collects 1/11th second of coder output (ten 1/110th second voice frames) for each packet.  The phone then adds 47B of Layer 2-6 overhead to each packet, at which point packets are placed on a 10 Mbps output line to a VoIP switch.  The switch is connected to a 1.7 Mbps output trunk with a 7 msec propagation delay, which in turn connects to a destination VoIP switch.  The destination VoIP switch in turn connects, via dedicated 10 Mbps output lines, to VoIP phones at the destination sink.  The VoIP phones contain de-jitter buffers to smooth out the packet arrivals, feeding phone bits to the sink voice decoder at regular intervals.  A block diagram of this system is shown below.



[15] Ignoring end-to-end delays, compute the number of VoIP phone calls that the 1.7 Mbps trunk can support.  [112 calls]
[20] If the maximum allowable mouth-to-ear (M2E) delay is 150 msec, estimate the number of VoIP calls this system can support based solely on end-to-end delay constraints.  Do a worst case analysis here.  Assume K VoIP phones generate K packets.  These K packets arrive simultaneously at the source VoIP switch at 110 msec intervals.  All packets must be played back at their respective sink phones within the M2E delay.  [41 calls]

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4) Given a four city ring with the working traffic matrix shown:
From/To Stillwater
 Tulsa
 Muskogee
 Oklahoma City
Stillwater
 -
 6
 8
 10
Tulsa
 4
 -
 2
 4
Muskogee
 10
 3
 -
 10
Oklahoma City
 7
 2
 2
 -

 
[20] If all traffic is routed around the ring in a clockwise direction, compute the working bandwidth required on each of the four links.  [okc to stillwater 28, stw to tulsa 31, tulsa to muskogee 30, muskogee to okc 41]
[20] Compute the minimum amount of additional protection bandwidth required on each of the four links to allow the ring to survive a single fiber cut.  In the event of a cut, disrupted traffic will be routed counter-clockwise.  [stw to okc 24, okc to muskogee 18, muskogee to tulsa 23, tulsa to stillwater 28]

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