多站平行等候模式 (M/M/C)：(N/∞/FCFS)

rm(list=ls()) options(digits=4) QueuingFullCapacity <- function(lamda, mu, numOfServant) { rho <- lamda / mu P0_1 <- (numOfServant * (rho ^ numOfServant)) / ((numOfServant - rho) * factorial(numOfServant)) P0_2 <- 0 for (i in 0:(numOfServant-1)) { P0_2 <- P0_2 + (rho ^ i) / (factorial(i)) } P0 <- 1/ (P0_1 + P0_2) Lq <- (P0 * numOfServant * (rho ^ (numOfServant+1))) /

(factorial(numOfServant) * ((numOfServant - rho) ^ 2)) Wq <- Lq / lamda W <- Wq + 1/mu L <- W * lamda ans <- c(rho, P0, L, W, Lq, Wq) ans } queuing <- function(lamda, mu, numOfServant, numOfCustomer, P0) { rho <- lamda / mu if (numOfCustomer < numOfServant) { Pn <- (P0 * (lamda ^ numOfCustomer)) / (factorial(numOfCustomer) * (mu ^ numOfCustomer)) } else { Pn <- (P0 * (lamda ^ numOfCustomer)) / (factorial(numOfServant) * (numOfServant ^ (numOfCustomer - numOfServant)) * (mu ^ numOfCustomer)) } ans <- Pn ans } avgNumOfCustomer <- 6 numOfRequestCanHold <- 3 numOfServant <-3 if (avgNumOfCustomer < numOfServant * numOfRequestCanHold) { ans <- QueuingFullCapacity(lamda=avgNumOfCustomer, mu=numOfRequestCanHold, numOfServant) P0 <- ans[2] print(sprintf("無客人機率=%.4f", P0)) print(sprintf("服務系統內平均客戶數=%.4f", ans[3])) print(sprintf("服務系統內平均處理時間=%.4f", ans[4])) print(sprintf("等候線內平均客戶數=%.4f", ans[5])) print(sprintf("等候線內平均處理時間=%.4f", ans[6])) Pn <- c(0, 0, 0) for (i in 1:numOfRequestCanHold) { Pn[i] <- queuing(lamda=avgNumOfCustomer, mu=numOfRequestCanHold, numOfServant=3, numOfCustomer=i, P0) print(sprintf("客人有 %d 人機率=%.4f", i, Pn[i])) } PanyCustomer <- 1 - (P0 + Pn[1] + Pn[2] + Pn[3]) print(sprintf("任一客戶等候機率=%.4f", PanyCustomer)) PanyServant <- P0 + Pn[1] + Pn[2] print(sprintf("任一服務者閒置機率=%.4f", PanyServant)) PparticularServant <- P0 + (Pn[1]*2)/numOfServant + Pn[2]/numOfServant print(sprintf("某一服務者閒置機率=%.4f", PparticularServant)) } else { print(sprintf("平均來客數=%d >= 服務者數=%d * 最大服務量=%d", avgNumOfCustomer, numOfServant, numOfRequestCanHold)) }