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maintained in lists After spawning all tasks, an accumulate (also known as reduction) operation can traverse the list sequentially, joining and using the results of each subtask Stretching the Fib example a bit, the FibVL class illustrates one way to set this up This style of solution is not especially useful here, but is applicable in contexts in which a dynamic number of subtasks are created, possibly across different methods Notice that the subtasks here are joined in the opposite order in which they were created Since the processing order of results does not matter here, we use the simplest possible linking algorithm (prepending), which happens to reverse the order of tasks during traversal This strategy applies whenever the accumulation step is commutative and associative with respect to results, so tasks can be processed in any order If the order did matter, we would need to adjust list construction or traversal accordingly

and at 0 otherwise. Then, if we observe the queue at the beginning of on periods, the queue length QP n evolves as follows (P stands for Palm probability [8]). QP QP r c ton ctoff ; n 1 n n n n ! 0: 10:12

Let F and F1 be the distribution and the integrated tail distribution, respectively, of ton . Theorem 10.4.1. P QP > x $ n If r > c, r c Eton < cEtoff , and F1 P s (or F P s*), then cEtoff r c r c Eton I

The peripheral driver software routines implement a state machine: 1. 2. 3. 4. When a channel is opened the peripheral is moved to the idle state If the peripheral is in the idle state when a request is made, it moves to the active state After the request is completed, the peripheral moves back to idle When in the idle state, the peripheral waits for a period of time (the inactivity timeout) and if no request is made, it moves to the retention state If the peripheral is in the retention state when a request is made, it moves to the active state When the null (or idle) thread runs, it calls a driver function which checks if the peripheral is idling, in which case the driver callback initiates the peripheral s move to retention state and cancels the inactivity timer. It also delays any device timeouts until the CPU wakes up If the peripheral is in one of the active, idle or retention states, the power manager may request a power down to either the standby or the off state The peripheral can only leave standby if the power manager requests a power up, in which case the driver software moves it to idle and starts the inactivity timer When the channel is closed, the driver software shuts down the peripheral (moving it to the off state).

class FibVL extends FJTask { volatile int number; // as before final FibVL next; // embedded linked list of sibling tasks FibVL(int n, FibVL list) { number = n; next = list; } public void run() { int n = number; if(n <= sequentialThreshold) number = seqFib(n); else { FibVL forked = null;

ACKNOWLEDGMENTS The author would like to thank Anna Gilbert, Jennifer Rexford, and Walter Willinger for many helpful discussions. Many of the traces considered in this chapter were collected using the tcp-dump packet capture tool developed by V. Jacobson, C. Leres, and S. McCanne and are available via anonymous ftp to ftp.ee.lbl.gov. To extract TCP connection information from the traces, we relied on V. Paxson's tcp-conn tool, which is available from http://ita.ee.lbl.gov/index.html. The DEC traces were collected by J. Mogul of Compaq's Western Research Lab (WRL), the LBL traces were gathered by V. Paxson and are available from http://www.acm.org/sigcomm/ITA, and we thank S. Alexander and S. Gao from AT&T Labs Research for making the MH and FP traf c collection possible. We also acknowledge the help of many of our colleagues at AT&T Labs, especially of J. Friedmann and A. Greenberg, with the data collection effort within WorldNet. Finally, we would like to thank P. Abry and D. Veitch for making their programs to perform the wavelet-based scaling analysis available to us. REFERENCES

5. 6.