Constructor Detail

Method Detail

• fj_respt_2way

   final static Double fj_respt_2way(Double lambda, Double mu)

  Exact two-way Fork-Join response time R_2^{F/J}(rho).

  Derived from Flatto and Hahn 1984: R_2^{F/J}(rho) = (H_2 - rho/8) * R(rho) = (12 - rho)/8 * R(rho)

  where H_2 = 1.5 and R(rho) = 1/(mu - lambda) is the M/M/1 mean response time.

  Parameters:

  lambda - Arrival rate

  mu - Service rate (mu lambda for stability)

  Returns:

  Exact 2-way F/J response time

• fj_respt_nt

   final static Double fj_respt_nt(Integer K, Double lambda, Double mu)

  Nelson-Tantawi approximation for K-way F/J response time.

  Valid for 2 <= K <= 32: R_K^{F/J}(rho) ~ H_K/H_2 + (1 - H_K/H_2) * 4*rho/11 * (1.5 - rho/8) / (mu - lambda)

  Parameters:

  K - Number of parallel servers (2 <= K <= 32)

  lambda - Arrival rate

  mu - Service rate (mu lambda for stability)

  Returns:

  Approximate K-way F/J response time

• fj_respt_vm

   final static Double fj_respt_vm(Integer K, Double lambda, Double mu)

  Varma-Makowski approximation for K-way F/J response time.

  R_K^{F/J}(rho) ~ H_K + (A_K - H_K) * rho * (mu - lambda)^{-1}

  where A_K = sum_{i=1}^{K} C(K,i) * (-1)^{i-1} * sum_{m=1}^{i} C(i,m) * (m-1)! / i^{m+1}

  Parameters:

  K - Number of parallel servers (positive integer)

  lambda - Arrival rate

  mu - Service rate (mu lambda for stability)

  Returns:

  Approximate K-way F/J response time

• fj_respt_varki

   final static Double fj_respt_varki(Integer K, Double lambda, Double mu)

  Varki et al. approximation for K-way F/J response time.

  Mean of pessimistic (upper) and optimistic (lower) bounds: R_K^{F/J}(rho) ~ (1/mu) * H_K + (rho/(2*(1-rho))) * (S1 + (1-2*rho)*S2)

  where: S1 = sum_{i=1}^{K} 1/(i - rho) S2 = sum_{i=1}^{K} 1/(i*(i - rho))

  Parameters:

  K - Number of parallel servers (positive integer)

  lambda - Arrival rate

  mu - Service rate (mu lambda for stability)

  Returns:

  Approximate K-way F/J response time