Q.1. Consider the network that is shown below. For all packets in this network,
ID: 3740504 • Letter: Q
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Q.1. Consider the network that is shown below. For all packets in this network, the packet sizes are exponentially distributed with an average size of 1000 bits/packet. All packet generation processes are Poisson processes. Ignore all propagation delays. Router 1 has 2 inputs, 2 outputs. Router 2 has 2 inputs and 1 output. Network 3D Link rate Link rate: 100kbps- 10 Kpackets/sec Router 2 A-spackets sec-Ragn ene HostA #1 0Kpackets/sec / 5Kpackets/sec Host B Network1 Network 2 _THI Host A generates packets with a rate of 2-5 packets/sec and sends them to Host B over Router 1 and Router 2. Traffic from Network I has a rate of ?,-10Kpackets/sec. 10% of these arrivals are routed to Network 3 and the rest ofthem go on thecomponenteoftheftalaverage delay tentfromHost AtoHostCaaaa0Pat to Router 2, Traffic from Network 2 has a rate of ?:"5Kpackets/sec. a) What are the components of the total average delay for a packet that is sent from Host A to Host B. b) What is the total average delay for a packet that is sent from Host A to Host B. Clearly specify all your assumptions and the properties that you use. C-100n0 Pa a) STOM2 /it_ ? ?, ? 10a0-10005, 15000-140045 7DM 1o 00 15000 o000000 o5+10000-1005 140015 10 000Pocket1000 t Sec | 1500 etla.ht, lalo‘Explanation / Answer
a) Let`s belive that we have sent some packets of fixed length through a network from Host A to Host B(through router1 to router 2), and also assume that routes of the packets do not change frequently. However, it`s from
problem statement that 10% of the total packet sent deviate through Network 3 due to some delay experienced when routing the packets to the destination. It`s observed that only random component that is responsible for the entire packet delay of the packet is due to the transmission distance and the speed it maintains during it`s transmisson on the network. Queuing delay is dependent on different packets that looks to be situated within buffers during it`s way to destination, and the nature of queuing delay is really unpredictable and random while processing the packets towards destination. We should observer that processing delay can also be treated random object, but tends to have less impact towards the packet delay as compared to queuing delay.
b) Let us consider all packets that is to be transmitted are of l bits, the transmission rate requires r bps for processing the packets and that n packets will be arrive at collectively at the queuing buffer for every ln/r seconds. However, it will take around ln/r seconds to send n packets towards destination. So, the buffer looks empty when the new group of n1 packets arrive in the queuing buffer. The first set of N packets will not experience any no queuing delay. The second set of N packets experience a queuing delay of l/r seconds. Overall, the Nth packet will experience a delay of (N1)*l/r seconds.
The following formula is used to explain about the total average delay experienced when sending the packets from one host to another host in the network:
1/n*Sigma(n to N=1)(N-1)*l/r= l/r*1/n*Sigma(n-1 to n=0)*n=l/r*1/n*(n-1)*n/2=l/r*(n-1)/2
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