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+41 votes
In a TDM medium access control bus LAN, each station is assigned one time slot per cycle for transmission. Assume that the length of each time slot is the time to transmit $100$ $\text{bits}$plus the end-to-end propagation delay. Assume a propagation speed of $2 \times 10^8 m/sec$. The length of the LAN is $1$ $\text{km}$ with a bandwidth of $10$ $\text{Mbps}$. The maximum number of stations that can be allowed in the LAN so that the throughput of each station can be $2/3$ $\text{Mbps}$is
  1. $3$
  2. $5$
  3. $10$
  4. $20$
in Computer Networks by Boss (16.3k points)
edited by | 5.3k views

Tt = 10 micro seconds
Tp = 5 micro seconds
In 15 microseconds 100 bits are sent. 
Throughput of the whole system  = total data sent per second

15 microseconds = 100 bits
= $\frac{100}{15}*10^6$ per second
we need n systems such that $n*\frac{2}{3}*10^6 \leq \frac{100}{15}*10^6 = 10$
Hence, (C) is the correct choice!

4 Answers

+58 votes
Best answer
$T_t = 10 \text{ micro secs}$

$T_p = 5 \text{ micro secs}$

Efficiency of the network $=\dfrac{T_t }{(T_t + T_p)}=\dfrac{10}{15}=\dfrac{2}{3}.$

Total throughput available for the entire network $=\text{Efficiency$\times $ Bandwidth}$
$=\dfrac{2}{3}\times 10 \text{ Mbps}=\dfrac{20}{3}\text{ Mbps}$

Let, No. of stations $=N\text{(each wants a Throughput of $\dfrac{2}{3}$ Mbps)},$

   $N\times \dfrac{2}{3}\text{ Mbps}=\dfrac{20}{3} \text{ Mbps}\Rightarrow N=10.$

$\Rightarrow 10$ stations can be connected in the channel at max.

Correct Answer: $C$
by Active (3.5k points)
edited by
how only the transmission time is useful time why not prapogation time...?
@bikram sir, Could you please help with the above doubt.


how only the transmission time is useful time why not prapogation time ?

efficiency or throughput  formula = transmission time / ( transmission time + propagation time )

here we say , Total time = transmission time + propagation time


Now Throughput means  the amount of data ( the whole message ) moved successfully from one place to another in a given time period . it is measured as bits per seconds bps ( how many bits transmit per seconds )or Kbps , Mbps  etc.. so it is measurement of whole number of bits ...

Where ,

Transmission time = This is the amount of time required to transmit all of the packet's bits into the link.

Propagation time = This is the time taken by a single bit ( MSB in general ) to reach from sender(A) to receiver(B).

As Transmission time is the time to transmit a whole packet( or total number of bits ) over a link , we consider it as useful time ..

and for total time we consider Transmission time + Propagation time .

Sir why are we multiplying by n.. In TDM medium access at each time slot is allotted to one station.So at any time the throughput of station should be equal to that of the link.. please correct me where I am going wrong.


see this line :

The maximum number of stations that can be allowed in the LAN so that the throughput of each station can be 2/3 Mbps is

If there are N stations and throughput of each station is 2/3 Mbps according to problem statement then maximum throughput = N * 2/3 

as it asking for maximum value, we need to multiply with N here..

ok now i got it. thank u sir
Why are we not taking throughput = TT/TT+2*PT . as we know total time is TT+ 2*PT where 2*PT is RTT time  please answer this i am very much confused.
This is TDM, here total cycle time is sum of transmission time and propagation time. In case of other sliding protocol mechanisms, we also consider the time for the data as well as ack to propagate and hence 2* propagation delay in 1 cycle
thanks :-)
can someone pls explain a practical scenario in which this can happen. Why no collision is occuring in this question when we multiply by N ?
+13 votes

Efficiency=useful time/total time

=transmission time/transmission +propagation time=10ms/(10ms+15ms)


so Effective bandwith utilized=(2/3)*10Mbps

Let there be N stations,throughput of each station should be 2/3 Mbps according to problem statement

so N *2/3 =Effective bandwith 

N*2/3=(2/3)  * 10


by Loyal (8.3k points)
this is correct.
+12 votes

For each station slot time is tx + tp(transmission time+prop. delay) 

tx = 100b/10Mbps = 10μs

tp = d/v = 5μs

So slot time is 15μs

If there are N stations then total cycle time is 15Nμ sec

efficiency will be useful time/total time ie (transmission time/total time) = (10μ/15Nμ) 

throughtput is eff*bandwidth => (10/15N)*10Mbps = (2/3)Mbps.

Solving this for N gives N as 10

Correct answer is 3

by Active (2.4k points)
@arjun sir . if i just find the efficency if one sytem is there it will be tt/tt+tp where tt is transmissin time and tp is propogation delay . so it will be 10/15 which is equal to 2/3 which means efficency with one system is 2/3 then it should be one system only. i think so .
some 1 cycle ie 15*N msec..why useful time is 10 micro sec..? shouldn't each station transmit..1 packet each n transmission time as 10*N ms?

total cycle time = T+Tp in TDM then why number of hosts are multiplied to calculate total cycle time

@Tendua 2/3 is the efficiency, but we need 2/3Mbps throughput as per question.

May be Beacuse Total Cycle Time is 15Nmicro_sec and In one Cycle a station can send only 10micro_sec thats why for  a single station its useful time is only 10micro_sec out of total cycle time which is 15Nmicro_sec.

that's why (10micro_sec/15Nmicro_sec)
+7 votes

Length of 1 time slot=Transmission time for 100 bits + propagation time (one-way).


$T_t(100\,bits\,)=\frac{100bits}{10^7bps}=10\mu s$

$T_p=\frac{10^3}{2*10^8}=5 \mu s$

Cycle time or 1 slot time=$15 \mu s$

Now in a TDM based channel access method, each node gets dedicated bandwidth of $\frac{R}{N} bps$ where 

R=Bandwidth of the broadcast medium

N=Total number of nodes in the network

For each node, the efficiency would be = $\frac{10}{15}=\frac{useful\,time}{total\,time}=\frac{2}{3}$

So, for each node the Throughput would be=Efficiency*Available Bandwidth=$\frac{2}{3}*\frac{10\,Mbps}{N}$

and this throghput is given in question i.e. $\frac{2}{3}$


N=10. Answer

by Boss (30.6k points)
@Ayush suppose say time is divided into 5 slots. There are 5 stations. They will be alloted slots in round robbin manner in each cycle. Suppose first slot is given to station 3, then it wil be able to use the bandwidth according to effective bandwidth as no other station is active in that slot for transmission. N *2/3 means all are simultaneously accessing the channel right?

Plz help me with this. Thanks
@tusharp-No No.Each node if given bandwidth of $\frac{R}{N}bps$ where the R=Total bandwidth of the channel and N is the number of stations and it is irrespective of whether any other stations is accessing the channel or not.(But it won't happen because each station is given a time slot).This is indeed the disadvantage of time multiplexed channel division where a node gets only portion of full bandwidth even though it is the only transmitting node.

Kurose Ross meh acha diya hai yeh. Padh lena ek bar :)
Thnx bhai... got it

@Ayush Upadhyaya I think the bandwidth of the channel should be same i.e. every node gets the same bandwidth(here 10Mbps) but its not all the nodes use it at the same time only the node which got the time slot will use it. Please correct me if I'm wrong.


@Hemanth_13-No.That each node gets R/N bps is disadvantage of the TDM as well as FDM.


@Ayush Upadhyaya Each node gets whole bandwidth of the channel.

Tdma from Forouzan Book
Screenshot from Behrouz A. Forouzan's Book



@Hemanth_13 You are right about your point on bandwidth. The main problem in this question is due to the difference in the meaning of throughput and bandwidth

Throughput: It is the amount of data that can be sent and received within a specific timeframe.

" So, if for one station throughput is then for stations throughput will be N*k. "


In TDMA, Throughput of the system = Effective Bandwidth = Efficiency * Bandwidth 


@nadeshseen-Bro, but Kurose Ross has a different story to it. 


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