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Official PYQ · 2008Q58Transport Layer: Flow Control, Congestion Control, UDP, TCP, SocketsMCQ1 mark

GATE CS 2008 Q58 — Transport Layer: Flow Control, Congestion Control, UDP, TCP, Sockets

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A computer on a 10Mbps10\text{Mbps} network is regulated by a token bucket. The token bucket is filled at a rate of 2Mbps2\text{Mbps}. It is initially filled to capacity with 16Megabits16\text{Megabits}. What is the maximum duration for which the computer can transmit at the full 10Mbps10\text{Mbps}?

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Answer: B

To find the maximum duration SS for which the computer can transmit at the maximum rate, we use the token bucket burst time formula.

Let:

  • C=16 MegabitsC = 16 \text{ Megabits} (Capacity of the token bucket)
  • ρ=2 Mbps\rho = 2 \text{ Mbps} (Token generation rate)
  • M=10 MbpsM = 10 \text{ Mbps} (Maximum transmission rate)
  • SS = Maximum burst duration (in seconds)

During the burst of duration SS seconds, the total volume of data transmitted at the full rate MM must equal the initial capacity of the bucket plus the new tokens accumulated during this interval:

M×S=C+ρ×SM \times S = C + \rho \times S

Rearranging the equation to solve for SS:

(M−ρ)×S=C(M - \rho) \times S = C S=CM−ρS = \frac{C}{M - \rho}

Substitute the given values into the formula:

S=16 Mb10 Mbps−2 Mbps=168=2 secondsS = \frac{16 \text{ Mb}}{10 \text{ Mbps} - 2 \text{ Mbps}} = \frac{16}{8} = 2 \text{ seconds}

Thus, the maximum duration for which the computer can transmit at the full 10 Mbps10\text{ Mbps} is 22 seconds.

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