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Chapter 6: Problem 8

In fair queuing, the value \(F_{i}\) was interpreted as a timestamp: the time when the \(i\) th packet would finish transmitting. Give an interpretation of \(F_{i}\) for weighted fair queuing, and also give a formula for it in terms of \(F_{i-1}\), arrival time \(A_{i}\), packet size \(P_{i}\), and weight \(w\) assigned to the flow.

Short Answer

Expert verified
In weighted fair queuing, \(F_i\) is the finish time of the \(i\)-th packet and is given by \(F_i = \text{max}(F_{i-1}, A_i) + \frac{P_i}{w}\).

Step by step solution

01

Understanding the Concept of Weighted Fair Queuing

In weighted fair queuing, flows are assigned different weights to represent their priority or share of the bandwidth. The timestamp for each packet is used to determine the order of transmission.
02

Interpreting the Timestamp in Weighted Fair Queuing

In weighted fair queuing, the timestamp label, denoted as \(F_i\), represents the time at which the \(i\)-th packet from a flow would finish transmitting, based on its weight.
03

Start With the Base Formula From Fair Queuing

In regular fair queuing, the finish time for the \(i\)-th packet is given by the formula: \[F_i = \text{max}(F_{i-1}, A_i) + P_i\].
04

Adjust the Formula for Weighted Fair Queuing

For weighted fair queuing, you need to account for the weight \(w\) of the flow. The effective service time for a packet in weighted fair queuing is scaled by the weight. The adjusted formula is given by: \[F_i = \text{max}(F_{i-1}, A_i) + \frac{P_i}{w}\].
05

Finalizing the Formula

Thus, the final formula for the finish time of the \(i\)-th packet in weighted fair queuing is: \[F_i = \text{max}(F_{i-1}, A_i) + \frac{P_i}{w}\].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

packet scheduling
Packet scheduling is a technique used in network systems to decide the order in which packets are transmitted over a network. In essence, it's about determining when and which packet to send next. This is crucial in ensuring efficient data flow and maintaining quality of service (QoS). Different scheduling algorithms can prioritize different aspects, such as reducing latency, increasing throughput, or ensuring fairness.

Weighted Fair Queuing (WFQ) is one such algorithm that aims to provide fair bandwidth allocation while allowing for different priorities among data flows. In WFQ, each flow of packets is given a weight. The weight represents the share of the bandwidth that the flow is expected to get. Packets from flows with higher weights are scheduled more frequently.

The exact scheduling of packets is determined using timestamps, which represent the virtual finishing time of packets if they were transmitted in a perfectly fair system. This helps decide which packet should be sent next, ensuring that the transmission is both fair and efficient.
bandwidth allocation
Bandwidth allocation is the process of distributing the available network bandwidth among different flows or users. Proper bandwidth allocation is essential for maintaining the performance and reliability of a network. In the context of Weighted Fair Queuing (WFQ), bandwidth allocation is determined by the weights assigned to each flow.

The weight of a flow determines how much bandwidth that flow is allowed to use compared to others. For instance, if a flow has a weight of 2 and another flow has a weight of 1, the first flow will get twice the amount of bandwidth compared to the second. This allows for creating priorities among different flows, ensuring that high-priority data like video calls receive more bandwidth than less critical data like background downloads.

The formula : ensures that the allocated bandwidth reflects the defined weights, making it fair yet efficient. Understanding how to control bandwidth allocation through WFQ helps network administrators optimize network performance based on the current usage and priorities.
network flows
Network flows refer to streams of packets between two network endpoints, such as a computer sending data to a server. These flows can vary in size, priority, and type of data transmitted. Managing network flows effectively is vital for maintaining high network performance and quality.

In Weighted Fair Queuing (WFQ), network flows are managed by assigning each flow a weight. These weights help in determining how packets from different flows are scheduled for transmission. Flows with higher weights receive more priority, meaning that their packets are more likely to be transmitted sooner than those with lower weights.

The formula : demonstrates how the finish time of a packet ( ) is calculated by considering the arrival time ( ), the size of the packet ( ), and the weight ( ) assigned to the flow. This helps maintain an organized and efficient network, allowing for a balance between different data types and requirements.

By understanding the role of network flows and how they are managed, especially through algorithms like WFQ, one can ensure a fair and high-performing network environment.

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Most popular questions from this chapter

Suppose two TCP connections share a path through a router R. The router's queue size is six segments; each connection has a stable congestion window of three segments. No congestion control is used by these connections. A third TCP connection now is attempted, also through R. The third connection does not use congestion control either. Describe a scenario in which, for at least a while, the third connection gets none of the available bandwidth, and the first two connections proceed with \(50 \%\) each. Does it matter if the third connection uses slow start? How does full congestion avoidance on the part of the first two connections help solve this?

Suppose host A reaches host B via routers R1 and R2: A-R1-R2-B. Fast retransmit is not used, and A calculates TimeOut as \(2 \times\) EstimatedRTT. Assume that the A-R1 and \(R 2-B\) links have infinite bandwidth; the \(R 1 \longrightarrow R 2\) link, however, introduces a 1 -second-per-packet bandwidth delay for data packets (though not ACKs). Describe a scenario in which the R1-R2 link is not \(100 \%\) utilized, even though A always has data ready to send. Hint: Suppose A's CongestionWindow increases from \(N\) to \(N+1\), where \(N\) is R1's queue size.

In TCP Vegas, the calculation of ActualRate is done by dividing the amount of data transmitted in one RTT interval by the length of the RTT. (a) Show that for any TCP, if the window size remains constant, then the amount of data transmitted in one RTT interval is constant once a full window is sent. Assume that the sender transmits each segment instantly upon receiving an ACK, packets are not lost and are delivered in order, segments are all the same size, and the first link along the path is not the slowest. (b) Give a timeline sketch showing that the amount of data per RTT above can be less than CongestionWindow.

Suppose a router's drop policy is to drop the highest-cost packet whenever queues are full, where it defines the "cost" of a packet to be the product of its size by the time remaining that it will spend in the queue. (Note that in calculating cost it is equivalent to use the sum of the sizes of the earlier packets in lieu of remaining time.) (a) What advantages and disadvantages might such a policy offer, compared to tail drop? (b) Give an example of a sequence of queued packets for which dropping the highest-cost packet differs from dropping the largest packet. (c) Give an example where two packets exchange their relative cost ranks as time progresses.

Consider a router that is managing three flows, on which packets of constant size arrive at the following wall clock times: flow A: \(1,2,4,6,7,9,10\) flow B: \(2,6,8,11,12,15\) flow C: \(1,2,3,5,6,7,8\) All three flows share the same outbound link, on which the router can transmit one packet per time unit. Assume that there is an infinite amount of buffer space. (a) Suppose the router implements fair queuing. For each packet, give the wall clock time when it is transmitted by the router. Arrival time ties are to be resolved in order \(\mathrm{A}, \mathrm{B}, \mathrm{C}\). Note that wall clock time \(T=2\) is FQ-clock time \(A_{i}=1.5\). (b) Suppose the router implements weighted fair queuing, where flows \(\mathrm{A}\) and \(\mathrm{B}\) are given an equal share of the capacity, and flow \(\mathrm{C}\) is given twice the capacity of flow A. For each packet, give the wall clock time when it is transmitted.
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