Package jline.examples.java.advanced

Class PassAndSwapCyclicExample

java.lang.Object
jline.examples.java.advanced.PassAndSwapCyclicExample
public class PassAndSwapCyclicExample extends Object
Validate the CTMC (exact) and LDES (simulation) solvers on a CLOSED CYCLIC network of two pass-and-swap (PAS / order-independent) queues against the exact product-form brute-force normalizing constant. Topology: --> Queue1 --> Queue2 --> (cyclic, R closed classes) PAS queues are order-independent, so the network is product-form. The brute force enumerates the whole ORDERED state space to obtain the normalizing constant G, hence exact per-class throughputs and mean queue lengths, which are compared against the solvers. Both stations must be valid OI queues: the TOTAL service rate mu_i(c) must depend only on the customer multiset. station 1: M/M/k OI queue, class-independent -> mu1(c) = min(n,k1)*s1 station 2: infinite-server, class-dependent -> mu2(c) = sum_j beta2[c_j] For station 2 the prefix sums depend on order, so the ordered-state enumeration is genuinely needed (it does not collapse to class counts). Class indices passed to mu(.) are 0-based (c(0) the oldest job).

  • Constructor Details

    • PassAndSwapCyclicExample

      public PassAndSwapCyclicExample()

  • Method Details

    • pas_cyclic_normconst_bruteforce

      public static double pas_cyclic_normconst_bruteforce()
      Brute-force normalizing constant of the closed cyclic PAS network (pas_cyclic_normconst_bruteforce.m).

      A pass-and-swap queue is an order-independent station: its total service rate is a function mu_i(c) of the ordered class sequence c at the station, and the stationary law is product-form and INVARIANT to the swap graph, so the swap graph is not needed here. G is obtained by splitting the population vector K into the per-class counts m at station 1 and K-m at station 2, then summing the OI balance function over every ordered arrangement of each station's count vector.

      Returns:
      the normalizing constant G at the full population

    • pas_cyclic_ctmc_vs_bruteforce

      public static void pas_cyclic_ctmc_vs_bruteforce()
      Validate CTMC and LDES against the exact brute-force product form (pas_cyclic_ctmc_vs_bruteforce.m).

    • main

      public static void main(String[] args)