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#171 data analysis + figures into report
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@taivop
taivop committed Dec 7, 2016
1 parent d0855b4 commit 946f4ad
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25 changes: 25 additions & 0 deletions report/milestone3.tex
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Expand Up @@ -151,6 +151,31 @@ \subsection{Model}

\subsection{Comparison of model and experiments}

\todo{}

\begin{figure}[h]
\centering
\includegraphics[width=0.5\textwidth]{../results/analysis/part2_mmm/graphs/traffic_intensity_vs_clients.pdf}
\caption{\todo{}}
\label{fig:part2:trafficintensity}
\end{figure}

\begin{figure}[h]
\centering
\includegraphics[width=\textwidth]{../results/analysis/part2_mmm/graphs/response_time_predicted_and_actual.pdf}
\caption{\todo{} note difference in scale}
\label{fig:part2:responsetime}
\end{figure}

\begin{figure}[h]
\centering
\includegraphics[width=\textwidth]{../results/analysis/part2_mmm/graphs/number_of_jobs_predicted_and_actual.pdf}
\caption{\todo{}}
\label{fig:part2:numberofjobs}
\end{figure}

\input{../results/analysis/part2_mmm/comparison_table.txt}


\clearpage
% --------------------------------------------------------------------------------
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14 changes: 14 additions & 0 deletions scripts/r/ms3_common.r
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Expand Up @@ -116,7 +116,21 @@ get_mmm_weird_rho <- function(m, rho, p0) {
return(p0 * (m * rho)^m / (factorial(m) * (1 - rho)))
}

get_mmm_response_time_mean <- function(rho, weird_rho, mu, m) {
return(1 / mu * (1 + weird_rho / (m * (1 - rho))))
}

get_mmm_response_time_std <- function(rho, weird_rho, mu, m) {
return(sqrt(1 / mu^2 * (1 + (weird_rho * (2 - weird_rho))/(m^2 * (1-rho)^2))))
}

get_mmm_num_jobs_in_system_mean <- function(rho, weird_rho, mu, m) {
return(m * rho + rho * weird_rho / (1 - rho))
}

get_mmm_num_jobs_in_system_std <- function(rho, weird_rho, mu, m) {
return(sqrt(m * rho + rho * weird_rho * ((1 + rho - rho * weird_rho)/((1 - rho)^2) + m)))
}



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109 changes: 88 additions & 21 deletions scripts/r/part2_mmm.r
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Expand Up @@ -32,7 +32,8 @@ get_mmm_summary <- function(results_dir) {
# ------------------
m <- 5
WINDOW_SIZE <- 1 # seconds
SAMPLING_RATE <- 10 # from exp2 setup
SAMPLING_RATE <- 100 # from exp1 setup
MAX_THROUGHPUT <- 26500 # from exp1: clients=576, repetition=0
service_rates <- requests %>%
mutate(secondCreated=floor(timeCreated/1000/WINDOW_SIZE)) %>%
group_by(secondCreated) %>%
Expand All @@ -41,7 +42,7 @@ get_mmm_summary <- function(results_dir) {

# ---- Parameters ----
arrival_rate <- mean(service_rates$count) / WINDOW_SIZE * SAMPLING_RATE
total_service_rate <- max(service_rates$count) / WINDOW_SIZE * SAMPLING_RATE
total_service_rate <- MAX_THROUGHPUT # max(service_rates$count) / WINDOW_SIZE * SAMPLING_RATE
single_service_rate <- total_service_rate / m
rho <- arrival_rate / total_service_rate # traffic intensity
p0 <- get_mmm_p0(m, rho) # prob. of 0 jobs in system
Expand All @@ -52,17 +53,23 @@ get_mmm_summary <- function(results_dir) {
# ---- Predictions ---- # TODO
predicted = list()
predicted$type <- "predicted"
predicted$mean_num_jobs_in_system <- m * rho + rho * weird_rho / (1 - rho)
predicted$std_num_jobs_in_system <-
m * rho + rho * weird_rho * ((1 + rho - rho * weird_rho)/((1 - rho)^2) + m)
predicted$mean_num_jobs_in_queue <- rho * weird_rho * (1 - rho)
predicted$traffic_intensity <- rho
predicted$num_jobs_in_system_mean <-
get_mmm_num_jobs_in_system_mean(rho, weird_rho, mu, m)
predicted$num_jobs_in_system_std <-
get_mmm_num_jobs_in_system_std(rho, weird_rho, mu, m)
predicted$num_jobs_in_queue_mean <- rho * weird_rho * (1 - rho)
predicted$utilisation <- rho
predicted$mean_response_time <-
1 / single_service_rate * (1 + weird_rho / (m * (1 - rho))) * 1000 # ms
predicted$response_time_mean <-
get_mmm_response_time_mean(rho, weird_rho, single_service_rate, m) * 1000 # ms
predicted$response_time_std <-
get_mmm_response_time_std(rho, weird_rho, single_service_rate, m) * 1000 # ms
Ew <- weird_rho / (m * single_service_rate * (1 - rho))
# predicted$mean_waiting_time <- Ew
predicted$response_time_q50 <- max(0, Ew / weird_rho * log(weird_rho / (1 - 0.5))) * 1000 # ms
predicted$response_time_q95 <- max(0, Ew / weird_rho * log(weird_rho / (1 - 0.95))) * 1000 # ms
predicted$arrival_rate <- NA
predicted$total_service_rate <- NA

# ---- Actual results ----
actual = list()
Expand All @@ -86,13 +93,17 @@ get_mmm_summary <- function(results_dir) {
response_times <- requests$timeReturned - requests$timeEnqueued

actual$type <- "actual"
actual$mean_num_jobs_in_system <- means$total
actual$std_num_jobs_in_system <- sum(distributions$total * (distributions$num_elements-means$total)^2)
actual$mean_num_jobs_in_queue <- means$queue
actual$utilisation <- 1 - (distributions %>% filter(num_elements==0))$total
actual$mean_response_time <- mean(response_times)
actual$traffic_intensity <- NA
actual$num_jobs_in_system_mean <- means$total
actual$num_jobs_in_system_std <- sum(distributions$total * (distributions$num_elements-means$total)^2)
actual$num_jobs_in_queue_mean <- means$queue
actual$utilisation <- NA # can't measure this on a per-server basis here
actual$response_time_mean <- mean(response_times)
actual$response_time_std <- sd(response_times)
actual$response_time_q50 <- quantile(response_times, probs=c(0.5))
actual$response_time_q95 <- quantile(response_times, probs=c(0.95))
actual$arrival_rate <- arrival_rate
actual$total_service_rate <- total_service_rate

comparison <- rbind(data.frame(predicted), data.frame(actual)) %>%
mutate(clients=result_params$clients[[1]],
Expand All @@ -107,15 +118,23 @@ result_dir_base <- "results/throughput"

# ---- Extracting data
dir_name_regex <- paste0(result_dir_base,
"/clients(\\d{2,3})_threads(32)_rep(0)$")
"/clients(\\d{1,3})_threads(32)_rep(0)$")
unfiltered_dirs <- list.dirs(path=result_dir_base, recursive=TRUE)
filtered_dirs <- grep(dir_name_regex, unfiltered_dirs, value=TRUE, perl=TRUE)

comparisons <- NA
for(i in 1:length(filtered_dirs)) {
dirname = filtered_dirs[i]
dirname_match <- grep(dir_name_regex, dirname, value=TRUE, perl=TRUE)
n_clients <- as.numeric(as.character(as.data.frame(str_match(dirname_match, dir_name_regex))$V2))
print(paste0("DIR: ", dirname))
summary <- get_mmm_summary(dirname)

if(n_clients == 1 | n_clients == 180 | n_clients > 576) {
print("skipping")
next
} else {
summary <- get_mmm_summary(dirname)
}

if(is.na(comparisons)) {
comparisons <- summary
Expand All @@ -124,12 +143,60 @@ for(i in 1:length(filtered_dirs)) {
}
}

# Saving table
comparisons_to_save <- comparisons %>%
select(type, clients, num_jobs_in_system_mean:response_time_std) %>%
select(-utilisation) %>%
melt(id.vars=c("type", "clients")) %>%
dcast(variable + clients ~ type)
comparison_table <- xtable(comparisons_to_save, caption="Comparison of experimental results and predictions of the M/M/m model.",
label="tbl:part2:comparison_table")
print(comparison_table, file=paste0(output_dir, "/comparison_table.txt"))


# ---- Plotting ----
data1 <- comparisons %>%
filter(clients != 180)
ggplot(data1, aes(x=clients, y=mean_response_time, color=type)) +
geom_line() +
asl_theme


# Traffic intensity
ggplot(comparisons %>% filter(type=="predicted"), aes(x=clients, y=traffic_intensity, color=type)) +
geom_line(size=1) +
geom_point(size=2) +
ylim(0, 1) +
xlab("Number of clients") +
ylab("Traffic intensity") +
asl_theme +
theme(legend.position="none")
ggsave(paste0(output_dir, "/graphs/traffic_intensity_vs_clients.pdf"),
width=fig_width/2, height=fig_height/2)

# Mean response time
ggplot(comparisons, aes(x=clients, y=response_time_mean, color=type, fill=type)) +
geom_ribbon(aes(ymin=response_time_mean-response_time_std,
ymax=response_time_mean+response_time_std),
alpha=0.3, color=NA) +
geom_line(size=1) +
geom_point(size=2) +
facet_wrap(~type, scales="free_y", nrow=1) +
#ylim(0, NA) +
xlab("Number of clients") +
ylab("Mean response time") +
asl_theme +
theme(legend.position="none")
ggsave(paste0(output_dir, "/graphs/response_time_predicted_and_actual.pdf"),
width=fig_width, height=0.75 * fig_height)

# Mean number of jobs in system
ggplot(comparisons, aes(x=clients, y=num_jobs_in_system_mean, color=type, fill=type)) +
geom_ribbon(aes(ymin=num_jobs_in_system_mean-num_jobs_in_system_std,
ymax=num_jobs_in_system_mean+num_jobs_in_system_std),
alpha=0.3, color=NA) +
geom_line(size=1) +
geom_point(size=2) +
facet_wrap(~type, nrow=1) +
ylim(0, NA) +
xlab("Number of clients") +
ylab("Mean number of jobs in system") +
asl_theme +
theme(legend.position="none")
ggsave(paste0(output_dir, "/graphs/number_of_jobs_predicted_and_actual.pdf"),
width=fig_width, height=0.75 * fig_height)

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