Here is the question. Suppose one bit stream arrives at a buffer. The rate of th
ID: 3887346 • Letter: H
Question
Here is the question. Suppose one bit stream arrives at a buffer. The rate of the bit stream is a periodic function of time with period T = 1 second. During [0, T/4], the rate is equal to 10 Mbps and during (T/4, T), it is equal to zero. A transmitter with rate R bps serves the buffer by sending the bits whenever available.
(a) Draw a diagram that shows the occupancy of the buffer as a function of time, for different ranges of values for R.
(b) What is the minimum value R0 of R so that this occupancy does not keep growing?
(c) For 10 R R0, express the average delay D(R) per bit as a function of R.
(d) For 10 R R0, express the average buffer occupancy (over time) L(R) as a function of R.
(e) Show that L(R) = D(R), where = 2.5 Mbps is the average arrival rate of the bits. This is an
example of the Little’s Formula.
arriving traffic from connection 1 buffer/queue arriving traffic from connection 2 server (link transmitter) Figure 3. A multiplexer that models one output link of a routerExplanation / Answer
The two switches are store-and-forward switches.
The two switches are sliced through switches. Note that a slice through switch does not sit tight for the whole bundle to touch base before it begins the transmission of the parcel. (Comment: as a general rule, there are sliced through switches rather than slice through switches. Be that as it may, for this issue, we accept there are sliced through switches.)
Assume
R 1=R2=R3== 1 Gbps (gigabits every second).. In any case, now,
R 1 = R 2 = 2 Mbps, and R 3 = 1 Mbps. Three parcels of a similar length, each with L = 1KB, are transmitted at the sender. What is the conclusion to-end defer of every parcel? For straightforwardness, you may disregard the handling time, which is little contrast and different postponements. Additionally, you require not tally parcels' holding up time at the sender.
For the circumstance in , draw a planning chart by finishing figure 2 and distinguish the queueing deferral of every parcel. Once more, you may disregard the handling time.
Issue 2 (20 focuses).
Rather than indicating the beginning and completion times of bundle transmission (e.g., Problem 1 (e)), an option method for depicting the activity creating process is to think the movement as a bit
R 2 R 3 R 1 Switch 1 Router 2 L Sender Receiver
Figure 1 Figure 2. Timing outline
parcel 2 bundle 1 time
In media communications and PC systems, multiplexing (now and again contracted to muxing) is a technique by which various simple or computerized signals are joined into one flag over a common medium. The point is to share a rare asset. For instance, in broadcast communications, a few phone calls might be conveyed utilizing one wire. Multiplexing began in telecommunication in the 1870s, and is presently broadly connected in correspondences. In communication, George Owen Squier is credited with the advancement of phone transporter multiplexing in 1910.The multiplexed flag is transmitted over a correspondence station, for example, a link. The multiplexing isolates the limit of the correspondence channel into a few legitimate channels, one for each message flag or information stream to be exchanged. A turn around process, known as demultiplexing, extricates the first channels on the collector end.A gadget that plays out the multiplexing is known as a multiplexer (MUX), and a gadget that plays out the invert procedure is known as a demultiplexer (DEMUX or DMX).
Converse multiplexing (IMUX) has the inverse point as multiplexing, in particular to break one information stream into a few streams, exchange them at the same time more than a few correspondence channels, and reproduce the first information stream. gadgets, a multiplexer (or mux) is a gadget that chooses one of a few simple or advanced info flags and advances the chose contribution to a solitary line.[1] A multiplexer of 2n inputs has n select lines, which are utilized to choose which input line to send to the output.[2] Multiplexers are fundamentally used to expand the measure of information that can be sent over the system inside a specific measure of time and bandwidth.[1] A multiplexer is additionally called an information selector. Multiplexers can likewise be utilized to actualize Boolean elements of various factors. An electronic multiplexer makes it feasible for a few signs to share one gadget or asset, for instance, one A/D converter or one correspondence line, rather than having one gadget for every info flag.
On the other hand, a demultiplexer (or demux) is a gadget taking a solitary info flag and choosing one of numerous information yield lines, which is associated with the single info. A multiplexer is regularly utilized with an integral demultiplexer on the accepting end.An electronic multiplexer can be considered as a different information, single-yield switch, and a demultiplexer as a solitary info, various yield switch. The schematic image for a multiplexer is an isosceles trapezoid with the more drawn out parallel side containing the information pins and the short parallel side containing the yield pin. The schematic on the correct demonstrates a 2-to-1 multiplexer on the left and a proportional switch on the privilege. The {displaystyle sel} sel wire associates the coveted contribution to the yield. Substance
1 Cost sparing
2 Digital multiplexers
2.1 Chaining multiplexers
2.2 List of ICs which give multiplexing
3 Digital demultiplexers
3.1 List of ICs which give demultiplexing
4 Multiplexers as PLDS
The fundamental capacity of a multiplexer: joining numerous contributions to a solitary information stream. On the getting side, a demultiplexer parts the single information stream into the first different signs.One use for multiplexers is streamlining associations over a solitary channel, by interfacing the multiplexer's single yield to the demultiplexer's single information. The picture to the privilege shows this advantage. For this situation, the cost of actualizing separate channels for every datum source is higher than the cost and burden of giving the multiplexing/demultiplexing capacities. At the less than desirable end of the information connect a corresponding demultiplexer is typically required to crush the single information stream spirit down into the first streams. Now and again, the far end framework may have usefulness more prominent than a straightforward demultiplexer; and keeping in mind that the demultiplexing still happens in fact, it might never be actualized discretely. This would be normal when: a multiplexer serves various IP arrange clients; and after that sustains straightforwardly into a switch, which promptly peruses the substance of the whole connection into its steering processor; and after that does the demultiplexing in memory from where it will be changed over specifically into IP segments.Regularly, a multiplexer and demultiplexer are joined together into a solitary bit of hardware, which is helpfully alluded to as a "multiplexer". Both circuit components are required at the two finishes of a transmission interface on the grounds that most correspondences frameworks transmit in the two headings. In simple circuit plan, a multiplexer is an exceptional kind of simple switch that associates one flag chose from a few contributions to a solitary yield.
In computerized circuit plan, the selector wires are of advanced esteem. On account of a 2-to-1 multiplexer, a rationale estimation of 0 would interface {displaystyle scriptstyle I_{0}} scriptstyle I_{0} to the yield while a rationale estimation of 1 would associate {displaystyle scriptstyle I_{1}} scriptstyle I_{1} to the yield. In bigger multiplexers, the quantity of selector pins is equivalent to {displaystyle scriptstyle leftlceil log _{2}(n) ight ceil } scriptstyle leftlceil log _{2}(n) ight ceil where {displaystyle scriptstyle n} scriptstyle n is the quantity of data sources. For instance, 9 to 16 information sources would require no less than 4 selector pins and 17 to 32 data sources would require no less than 5 selector pins. The double esteem communicated on these selector pins decides the chose input stick. A 2-to-1 multiplexer has a boolean condition where {displaystyle scriptstyle A} scriptstyle An and {displaystyle scriptstyle B} scriptstyle B are the two data sources, {displaystyle scriptstyle S} scriptstyle S is the selector input, and {displaystyle scriptstyle Z} scriptstyle Z is the yield:
{displaystyle Z=(Acdot {overline {S}})+(Bcdot S)} Z=(Acdot {overline {S}})+(Bcdot S)
A 2-to-1 mux
Which can be communicated as a reality table:
{displaystyle scriptstyle S} scriptstyle S {displaystyle scriptstyle A} scriptstyle A {displaystyle scriptstyle B} scriptstyle B {displaystyle scriptstyle Z} scriptstyle Z
0 0 0 0
0 0 1 0
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 1
1 1 0 0
1 1 1 1
packets'queue'in'router'buffers''
• packet'arrival'rate'to'link'exceeds'output'link'capacity'
• packets'queue,'wait'for'turn'
A
B
packet'being'transmiBed'(delay)'
packets'queueing'(delay)
free'(available)'buffers:'arriving'packets'
dropped'(loss)'if'no'free'buffers1. Nodal'processing:''
– check'bit'errors'
– determine'output'link'
2. Queueing
– output'link'for' transmission''
-depends'on'congesKon'level'of' switch'
3. Transmission'delay:'
– aka'store'&'forward'delay'
– R=link'bandwidth'(bps)'
– L=packet'length'(bits)'
– Kme'to'send'bits'into'link'='L/R'
2. PropagaKon'delay:'
– d'='length'of'physical'link'
– s'='propagaKon'speed'in'medium'
(~2x108 m/sec)'
– propagaKon'delay'='d/s
A
B
proliferation transmission nodal preparing queueing.