Consider a router Adirectly connected ton hosts. Router Ais also connected to an

Question

Consider a router Adirectly connected ton hosts. Router Ais also connected to an ISP’srouter B. Thelink between A and B has capacity 1Gbps. Each host, when active, uploads datato A (andthen A forwards to B to the outside world) at rate10 Mbps.However, at any given hour, the probability that a given host isactive is only p =0.1. Ifcircuit switching is used, what is the maximum number of hosts(say n = n0)that can be supported by this network setting? I'm getting 1000Mbps / 10Mbps = 100 concurrenthosts. However, I am not sure if the probability should be factoredin resulting in the network being able to support 1000 hosts, ofwhich 100 are active. Please advise. Thank you. Consider a router Adirectly connected ton hosts. Router Ais also connected to an ISP’srouter B. Thelink between A and B has capacity 1Gbps. Each host, when active, uploads datato A (andthen A forwards to B to the outside world) at rate10 Mbps.However, at any given hour, the probability that a given host isactive is only p =0.1. Ifcircuit switching is used, what is the maximum number of hosts(say n = n0)that can be supported by this network setting? I'm getting 1000Mbps / 10Mbps = 100 concurrenthosts. However, I am not sure if the probability should be factoredin resulting in the network being able to support 1000 hosts, ofwhich 100 are active. Please advise. Thank you. I'm getting 1000Mbps / 10Mbps = 100 concurrenthosts. However, I am not sure if the probability should be factoredin resulting in the network being able to support 1000 hosts, ofwhich 100 are active. Please advise. Thank you.

Explanation / Answer

The probability p=0.1 should be factored in to yourcalculation. Therefore this network can support 1000 hosts out of which only 100hosts are active at any given hour.

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