Computer Science Department, Bucknell University

Formulas for CSCI 320 Final exam

December 13, 2007
  1. CPU time = Instruction Count x Clock cycles per instruction x Clock cycle time [page 42]

  2. Amdahl's Law: Speedupoverall = Execution timeold / Execution timenew =

    1/((1 - Fractionenhanced) + (Fractionenhanced/Speedupenhanced)) [page 39]

  3. Average memory access time = Hit time + Miss rate x Miss penalty [page C-15]

  4. CPU time = IC x (CPIexecution+ Memory accesses/Instruction x Miss rate x Miss penalty) x Clock cycle time [page C-18]

  5. Little's Law: Mean number of tasks in system = Arrival rate x Mean response time

    Assuming the system is in equilibrium [page 380]

  6. Server utilization = mean arrival rate x mean server time [page 381]

    Assumes one server.

  7. Timequeue = Lengthqueue x Timeserver +1/2 x server utilization x Weighted Mean time x (1 + C2)

    Assumes FIFO queue and exponential interarrival times. Time is just after the new arrival is placed in queue. [page 384]

    C2 = Variance/Weighed Mean Time2 [page 383]

    Variance = (F1 x T12 + F2 x T22 + ... Fn x Tn2) - Weighed Mean Time2 [page 383]

  8. Timequeue = Timeserver x Server utilization /(1 - Server utilization)

    Assumes FIFO and exponential distribution of server rates [page 387]