Question

2. please provide the right solution regarding leaky buckets

Exercise 1.3.2 1. Draw the arrival curve for a linearly constrained flow with parameters (m, b) that also has a limit o


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Exercise 1.3.2 1. Draw the arrival curve for a linearly constrained flow with parameters (m,b) that also has a limit on the peak rate. What is the arrival curve? 2. Show that a flow is (P,B) constrained iff W
P
​
(t)≤B for all t

Answer 1

Leaky bucket is a queueing model used to control and regulate the flow of data in a network. In this model, data packets are treated as water flowing into a bucket. The bucket has a hole in the bottom, which represents the data rate of the network. If the data rate is greater than the hole size, the bucket will overflow.

Exercise 1.3.2:

1. The arrival curve for a linearly constrained flow with parameters (m,b) that also has a limit on the peak rate is given by:

a(t) = min(mt + b, p)

where a(t) is the arrival curve, m is the slope of the linear constraint, b is the intercept of the linear constraint, and p is the peak rate limit.

2. A flow is (P,B) constrained iff W(P)(t) ≤ B for all t, where W(P)(t) is the backlog function of the flow and B is the buffer size of the network. The backlog function is defined as the amount of data that has arrived but has not yet been transmitted. If the backlog function is greater than the buffer size, the network will become congested. Therefore, a flow is (P,B) constrained if it satisfies the condition that the backlog function is less than or equal to the buffer size for all t.