A stage of an n × n banyan network consists of (n/2) 2 × 2 switching elements. The first stage directs packets to the correct half of the network, the next stage to the correct quarter, and so on, until the packet is routed to the correct output. Derive an

A stage of an n × n banyan network consists of (n/2) 2 × 2 switching elements. The first stage directs packets to the correct half of the network, the next stage to the correct quarter, and so on, until the packet is routed to the correct output. Derive an

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.10: Exponential Queues In Series And Open Queuing Networks

Problem 8P

See similar textbooks

Similar questions

A factor in the delay of a store-and-forward packet-switching system is how long it takes to store and forward a packet through a switch. If switching time is 10 usec, is this likely to be a major factor in the response of a client-server system where the client is in New York and the server is in California? Assume the propagation speed in copper and fiber to be 2/3 the speed of light in vacuum.
How long does it take a packet of length 1,000 bytes to propagate over a link of distance 2,500 km, propagation speed 25.125 m/s, and transmission rate 2 Mbps? More generally, how long does it take a packet of length L to propagate over a link of distance d, propagation speed s, and transmission rate R bps? Does this delay depend on packet length? Does this delay depend on transmission rate?
Suppose a system has 50 MB data to send on a network and transmit the data in burst at 8 Mbps, the maximum transmission rate across routers in the network is 6 Mbps, if system uses leaky bucket algorithm, the capacity (in MB) that bucket must hold so that no data is discarded is?.
In this example, assume that the fixed path is used to transport a packet from a source to an address at the other end of the network. List the many components of delay as well: Approximately how many delays are continuous for how long, and approximately how many are timedependent?
Consider a packet of length L which begins at end system A and travels over three links to a destination end system. These three links are connected by two packet switches. Let di, si, and Ri denote the length, propagation speed, and the transmission rate of link i, for i = 1, 2, 3. The packet switch delays each packet by dproc. Assuming no queuing delays, in terms of di, si, Ri, (i = 1,2,3), and L, what is the total end-to-end delay for the packet? Suppose now the packet is 1,500 bytes, the propagation speed on all three links is 2.5*108 m/s, the transmission rates of all three links are 2 Mbps, the packet switch processing delay is 3 msec, the length of the first link is 5,000 km, the length of the second link is 4,000 km, and the length of the last link is 3,000 km. For these values, what is the end-to-end delay?
How long does it take a packet of length 1,000 bytes to propagate over a link of distance 5,000 km, propagation speed of 2.5 x 108 m/s, transmission rate 1 Mbps? Generally, how long does it take a packet of length L to propagate over a link of distance d, propagation speed s, and transmission rate R bps? Does this delay depend on packet length? Does this delay depend on transmission rate?
Consider a packet of length L that begins at end system A and travels over three links to a destination end system. These three links are connected by two packet switches. Let di, si, and Ri denote the length, propagation speed, and the transmission rate of link i, for i=1,2,3. The packet switch delays each packet by dproc. Assuming no queuing delays, in terms of di, si, Ri, (i=1,2,3), and L, what is the total end-to-end delay for the packet? Suppose now the packet is 1,200 bytes, the propagation speed on all three links is 2.5x10^8 m/s, the transmission rates of all three links are 2 Mbps, the packet switch processing delay is 3 msec, the length of the first link is 4,000 km, the length of the second link is 3,000 km, and the length of the last link is 1,500 km. For these values, what is the end-to-end delay? In the above problem, suppose R1=R2=R3=R and dproc=0. Further suppose the packet switch does not store-and-forward packets but instead immediately transmits each bit it receives…
A packet switch receives a packet and determines the outbound link to which the packet should be forwarded. When the packet arrives, one other packet is halfway done being transmitted on this outbound link and four other packets are waiting to be transmitted. Packets are transmitted in order of arrival. Suppose all packets are 1,200 bytes and the link rate is 2 Mbps. What is the queuing delay for the packet? More generally, what is the queuing delay when all packets have length L, the transmission rate is R, x bits of the currently-being-transmitted packet have been transmitted, and n packets are already in the queue?
To get around the problem of sequence numbers wrapping around while old packets still exist, one could use 64-bit sequence numbers. However, theoretically, an optical fiber can run at 75 Tbps. What maximum packet lifetime is required to make sure that future 75 Tbps networks do not have wraparound problems even with 64-bit sequence numbers? Assume that each byte has its own sequence number. as TCP does.
This elementary problem begins to explore propagation delay and transmission delay, two central concepts in data networking. Consider two hosts, A and B, connected by a single link of rate R bps. Suppose that the two hosts are separated by m meters, and suppose the propagation speed along the link is s meters/sec. Host A is to send a packet of size L bits to Host B. a. Express the propagation delay, dprop, in terms of m and s.b. Determine the transmission time of the packet, dtrans, in terms of L and R.c. Ignoring processing and queuing delays, obtain an expression for the end-to-end delay.d. Suppose Host A begins to transmit the packet at time t = 0. At time t = dtrans, where is the last bit of the packet?e. Suppose dprop is greater than dtrans. At time t = dtrans, where is the first bit of the packet?f. Suppose dprop is less than dtrans. At time t = dtrans, where is the first bit of the packet?g. Suppose s = 2.5 * 108 meters/sec, L = 120 bits, and R = 0.112 Mbps. Find the distance m…
This elementary problem begins to explore propagation delay and transmission delay, twocentral concepts in data networking. Consider two hosts, A and B, connected by a single link ofrate R bps. Suppose that the two hosts are separated by m meters, and suppose the propagationspeed along the link is s meters/sec. Host A is to send a packet of size L bits to Host B.a. Express the propagation delay, dprop, in terms of m and s.b. Determine the transmission time of the packet, dtrans, in terms of Land R.c. Ignoring processing and queuing delays, obtain an expression for the endto-end delay.d. Suppose Host A begins to transmit the packet at time t = 0. At time t = dtrans,where is the last bit of the packet?e. Suppose dprop is greater than dtrans. At time t = dtrans, where is the first bit ofthe packet?f. Suppose dprop is less than dtrans. At time t = dtrans, where is the first bit ofthe packet?g. Suppose s = 2.5 · 108, L = 120 bits, and R = 56 kbps. Find the distance mso that dprop equals…
This elementary problem begins to explore propagation delay andtransmission delay, two central concepts in data networking. Consider two hosts, Aand B, connected by a single link of rate R bps. Suppose that the two hosts areseparated by m meters, and suppose the propagation speed along the link is smeters/sec. Host A is to send a packet of size L bits to Host B. d. Suppose Host A begins to transmit the packet at time t=0 . At time t= ?????? ,where is the last bit of the packet? e. Suppose ????? is greater than ?????? . At time t= ??????, where is the first bit of the packet?f. Suppose ????? is less than ??????. At time t= ?????? , where is the first bit of thepacket?