基本等候模式 (M/M/1)：(N/∞/FCFS)

rm(list=ls()) options(digits=4) QueuingFullCapacity <- function(lamda, mu, maxNumOfCustomer) { rho <- lamda / mu if (rho==1) { P0 <- 1 / (maxNumOfCustomer + 1) Pn <- P0 L <- maxNumOfCustomer / 2 } else { P0 <- (1 - rho) / (1 - rho ^ (maxNumOfCustomer + 1)) Pn <- P0 * rho ^ maxNumOfCustomer L <- (rho / (1 - rho)) - ((maxNumOfCustomer + 1)*rho ^ (maxNumOfCustomer + 1) / (1 - rho ^ (maxNumOfCustomer + 1))) } Lq <- P0 + L - 1 W <- L / (lamda * (1 - Pn)) Wq <- Lq / (lamda * (1 - Pn)) ans <- c(rho, P0, Pn, L, W, Lq, Wq) ans } queuing <- function(lamda, mu, maxNumOfCustomer, numOfCustomer, P0, L) { rho <- lamda / mu if (rho==1) { Pn <- P0 } else { Pn <- P0 * rho ^ numOfCustomer } Lq <- P0 + L - 1 W <- L / (lamda * (1 - Pn)) Wq <- Lq / (lamda * (1 - Pn)) ans <- c(rho, P0, Pn, L, W, Lq, Wq) ans } avgNumOfCustomer <- 2 numOfRequestCanHold <- 3 ans <- QueuingFullCapacity(lamda=avgNumOfCustomer, mu=numOfRequestCanHold, maxNumOfCustomer=3) P0 <- ans[2] L <- ans[4] print(sprintf("無客人機率=%.4f", P0)) print(sprintf("服務系統內平均客戶數=%.4f", ans[4])) print(sprintf("服務系統內平均處理時間=%.4f", ans[5])) print(sprintf("等候線內平均客戶數=%.4f", ans[6])) print(sprintf("等候線內平均處理時間=%.4f", ans[7])) ans <- queuing(lamda=2, mu=3, maxNumOfCustomer=3, numOfCustomer=1, P0, L) print(sprintf("客人等待機率=%.4f", 1- ans[2] - ans[3])) for (i in 1:2) { ans <- queuing(lamda=2, mu=3, maxNumOfCustomer=3, numOfCustomer=i, P0, L) print(sprintf("客人有 %d 人機率=%.4f", i, ans[3])) }