queueing-simulation-r/queuing_simulation.Rmd at main · DevAime/queueing-simulation-r · GitHub

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---
title: "Untitled"
author: "Aime Muganga"
date: "2025-03-13"
output: html_document
---


```{r}
library(queueing)

lambda_rate <- 5  # Arrival rate
mu_rate <- 3      # Service rate

# Simulate M/M/c model for c in range 1 to 5
for (c in 1:5) {
  if (lambda_rate / (mu_rate * c) >= 1) {
    print(paste("Skipping c =", c, "as system would be unstable."))
  } else {
    mmc_model <- QueueingModel(NewInput.MMC(lambda=lambda_rate, mu=mu_rate, c=c))
    print(paste("Results for c =", c))
    print(summary(mmc_model))  # Prints the key performance metrics
    cat(rep("-", 40), "\n")
  }
}
```

```{r}
library(queueing)
lambda_rate <- 5  # Arrival rate
mu_rate <- 7
servers <- 1:5
SU<-lambda_rate/(c*mu_rate)
results <- data.frame(Servers=servers,L=NA, Wq=NA, SU=NA,ID=NA)

for (c in servers){
  MMC_input<-NewInput.MMC(lambda=lambda_rate,mu=mu_rate)
  MMC_Model<-QueueingModel(MMC_input)
  MMC_Model$L
  results$L[results$Servers==c]<-MMC_Model$L
  results$Wq[results$Servers==c]<-MMC_Model$Wq
  results$SU[results$Servers==c]<-SU
  results$ID[results$Servers==c]<-1-SU

}
results

```

```{r}
library(queueing)
library(ggplot2)

lambda_rate <- 5  # Arrival rate
mu_rate <- 7      # Service rate
servers <- 1:5

# Create an empty dataframe
results <- data.frame(Servers=servers, L=NA, Wq=NA, SU=NA, ID=NA)

for (c in servers) {
  # Compute server utilization inside the loop
  SU <- lambda_rate / (c * mu_rate)

  # Ensure 'c' is passed correctly when defining the queueing model
  MMC_input <- NewInput.MMC(lambda=lambda_rate, mu=mu_rate, c=c)
  MMC_Model <- QueueingModel(MMC_input)

  # Store the results in the dataframe
  results$L[results$Servers == c] <- MMC_Model$L
  results$Wq[results$Servers == c] <- MMC_Model$Wq
  results$SU[results$Servers == c] <- SU
  results$ID[results$Servers == c] <- 1 - SU
}

# Plot c against L
ggplot(results, aes(x=Servers, y=L)) +
  geom_line(color='blue') +
  geom_point(color='red') +
  labs(title='Queue Length (L) vs Number of Servers (c)',
       x='Number of Servers (c)',
       y='Queue Length (L)') +
  theme_minimal()

# Plot c against Wq
ggplot(results, aes(x=Servers, y=Wq)) +
  geom_line(color='green') +
  geom_point(color='orange') +
  labs(title='Waiting Time (Wq) vs Number of Servers (c)',
       x='Number of Servers (c)',
       y='Waiting Time (Wq)') +
  theme_minimal()

# Plot c against SU (Service Utilization)
ggplot(results, aes(x=Servers, y=SU)) +
  geom_line(color='purple') +
  geom_point(color='pink') +
  labs(title='Service Utilization (SU) vs Number of Servers (c)',
       x='Number of Servers (c)',
       y='Service Utilization (SU)') +
  theme_minimal()

# Plot c against ID (Idle Time)
ggplot(results, aes(x=Servers, y=ID)) +
  geom_line(color='brown') +
  geom_point(color='yellow') +
  labs(title='Idle Time (ID) vs Number of Servers (c)',
       x='Number of Servers (c)',
       y='Idle Time (ID)') +
  theme_minimal()

# Print results
print(results)

```

```{r}
library(queueing)
library(ggplot2)

lambda_rate <- 5  # Arrival rate (per hour)
mu_rate <- 7      # Service rate (per hour)
time_period <- 10 # Simulation period in hours
servers <- 1:5

# Create an empty dataframe
results <- data.frame(Servers=servers, Total_L=NA, Total_Wq=NA, SU=NA, ID=NA)

for (c in servers) {
  # Compute server utilization inside the loop
  SU <- lambda_rate / (c * mu_rate)

  # Ensure 'c' is passed correctly when defining the queueing model
  MMC_input <- NewInput.MMC(lambda=lambda_rate, mu=mu_rate, c=c)
  MMC_Model <- QueueingModel(MMC_input)

  # Store the results in the dataframe
  results$Total_L[results$Servers == c] <- MMC_Model$L * time_period  # Accumulated customers over 10 hours
  results$Total_Wq[results$Servers == c] <- MMC_Model$Wq * (lambda_rate * time_period)  # Total waiting time
  results$SU[results$Servers == c] <- SU
  results$ID[results$Servers == c] <- 1 - SU
}

# Plot c against Total_L
ggplot(results, aes(x=Servers, y=Total_L)) +
  geom_line(color='blue') +
  geom_point(color='red') +
  labs(title='Total Queue Length over 10 Hours vs Number of Servers',
       x='Number of Servers (c)',
       y='Total Queue Length (L * 10)') +
  theme_minimal()

# Plot c against Total_Wq
ggplot(results, aes(x=Servers, y=Total_Wq)) +
  geom_line(color='green') +
  geom_point(color='orange') +
  labs(title='Total Waiting Time over 10 Hours vs Number of Servers',
       x='Number of Servers (c)',
       y='Total Waiting Time (Wq * 50)') +
  theme_minimal()

# Plot c against SU (Service Utilization)
ggplot(results, aes(x=Servers, y=SU)) +
  geom_line(color='purple') +
  geom_point(color='pink') +
  labs(title='Service Utilization vs Number of Servers',
       x='Number of Servers (c)',
       y='Service Utilization (SU)') +
  theme_minimal()

# Plot c against ID (Idle Time)
ggplot(results, aes(x=Servers, y=ID)) +
  geom_line(color='brown') +
  geom_point(color='yellow') +
  labs(title='Idle Time vs Number of Servers',
       x='Number of Servers (c)',
       y='Idle Time (ID)') +
  theme_minimal()

# Print results
print(results)

```