## How many cells were sent by the source in time interval [0, 401] ?

In this problem, time is counted in slots. One slot is the duration to transmit one ATM cell on the link.

1.       An ATM source S1 is constrained by GCRA(T = 50 slots, τ = 500 slots), The source sends cells according to the following algorithm.

• In a first phase, cells are sent at times t(1) = 0, t(2) = 10, t(3) = 20,…,t(n) = 10(n − 1) as long as all cells are conformant. In other words, the number n is the largest integer such that all cells sent at times t(i) = 10(i − 1), i ≤ n are conformant. The sending of cell n at time t(n) ends the first phase.

• Then the source enters the second phase. The subsequent cell n + 1 is sent at the earliest time after t(n) at which a conformant cell can be sent, and the same is repeated for ever. In other words, call t(k) the sending time for cell k, with k>n; we have then: t(k) is the earliest time after t(k − 1) at which a conformant cell can be sent.

How many cells were sent by the source in time interval [0, 401] ?

2.       An ATM source S2 is constrained by both GCRA(T = 10 slots, τ = 2 slots) and GCRA(T = 50 slots, τ = 500 slots). The source starts at time 0, and has an infinite supply of cells to send. The source sends its cells as soon as it is permitted by the combination of the GCRAs. We call t(n) the time at which the source sends the nth cell, with t(1) = 0. What is the value of t(15) ?

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