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(a) The transmission time of a bit or group of bits is sometimes referred to as their "width" on the line. What is the width of an L-frame on a LAN link? (b) How wide is an L-frame (as embedded inside larger frames) on a MAN link?

(a) The transmission time of a bit or group of bits is sometimes referred to as their "width" on the line. What is the width of an L-frame on a LAN link? (b) How wide is an L-frame (as embedded inside larger frames) on a MAN link?

Operations Research : Applications and Algorithms
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
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1. A protocol uses hierarchical slotted TDM techniques for various levels of networks. For the purpose of this question, assume header/trailer overhead to be zero, use the different DLC frame sizes as given. In this question we consider only DLC frames. At the level of Local Area Networks (LANS) containing each individual computer, the links operate at 10 Mbps and the frames (L-frames) are each 1500 bytes long. The LANs link to Metropolitan Area Networks (MANS) which use 15000 byte M-frames that are made by multiplexing 10 L-frames, one each from 10 different LANs. Every ten of these MANS feed into a Regional Area Network (RAN) that uses 1 Gbps links and uses a R- frame, and ten RANS feed into a Wide Area Network (WAN) using a W-frame, which is 32 times the size of an R-frame. (a) The transmission time of a bit or group of bits is sometimes referred to as their "width" on the line. What is the width of an L-frame on a LAN link? (b) How wide is an L-frame (as embedded inside larger frames) on a MAN link? (c) What is the ratio (e.g. 2:1) of TDM of L-frames into R-frames? (d) If the MAN links are exactly fast enough to allow M-frames to be sent at a rate that does not require any of the LANs to slow down (or cause a buffer to build up at the intermediate node connecting the LANs to the MAN) what is the bitrate of the MAN links? (e) If the RAN transmits one R-frame in the same amount of time that a LAN transmits one L-frame, what fraction, if any, of the R-frame bits is wasted? (f) If a WAN link is 64 times faster than a RAN link, what is the TDM ratio of R-frames into W-frames? (g) What fraction, if any, of the W-frame bits is wasted?
Transcribed Image Text:1. A protocol uses hierarchical slotted TDM techniques for various levels of networks. For the purpose of this question, assume header/trailer overhead to be zero, use the different DLC frame sizes as given. In this question we consider only DLC frames. At the level of Local Area Networks (LANS) containing each individual computer, the links operate at 10 Mbps and the frames (L-frames) are each 1500 bytes long. The LANs link to Metropolitan Area Networks (MANS) which use 15000 byte M-frames that are made by multiplexing 10 L-frames, one each from 10 different LANs. Every ten of these MANS feed into a Regional Area Network (RAN) that uses 1 Gbps links and uses a R- frame, and ten RANS feed into a Wide Area Network (WAN) using a W-frame, which is 32 times the size of an R-frame. (a) The transmission time of a bit or group of bits is sometimes referred to as their "width" on the line. What is the width of an L-frame on a LAN link? (b) How wide is an L-frame (as embedded inside larger frames) on a MAN link? (c) What is the ratio (e.g. 2:1) of TDM of L-frames into R-frames? (d) If the MAN links are exactly fast enough to allow M-frames to be sent at a rate that does not require any of the LANs to slow down (or cause a buffer to build up at the intermediate node connecting the LANs to the MAN) what is the bitrate of the MAN links? (e) If the RAN transmits one R-frame in the same amount of time that a LAN transmits one L-frame, what fraction, if any, of the R-frame bits is wasted? (f) If a WAN link is 64 times faster than a RAN link, what is the TDM ratio of R-frames into W-frames? (g) What fraction, if any, of the W-frame bits is wasted?
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