Revisiting the LogGPS model for simulation purposes

   read_csv <- function(file) {
     df <- read.csv(file, header=FALSE, strip.white=TRUE)
     names(df) <- c("Nature","ResourceId","Type","Start","End","Duration","Imbrication","Value")
     df = df[!(names(df) %in% c("Nature","Type", "Imbrication"))]
     df$Origin=file
     df
   }
   
   df_values <- read_csv('simgrid_graphene_switch2_4344.csv')

This comprises three sets of experiments:

1. One for determining o_s and o_r using MPI_Send and MPI_Recv
2. Its counterpart for determining the MPI_I* o_s and o_r
3. One for determining L and g|G with sequence of ping pong

Message size in all three sets of experiments are randomized to avoid bias.

  basic_plot(df_send)

  classify_messages <- function(d, col_bound) {
    d$group=as.character("outliers")
    for(i in (1:length(bp$Limit))) {
        d[d$Size < bp[i,]$Limit & d$Size >= bp[i,]$LimitInf & d$Duration<bp[i,col_bound],]$group = bp[i,]$Name
    }
    d
  }

  compute_lm <- function(bp, d, zone,remove_sync=FALSE,remove_detached=FALSE) {
    if(remove_sync) { 
       group_list = bp[bp$Limit<=detached_threshold,]$Name
    } else {
       group_list = bp$Name
    }
    if(remove_detached) {
       group_list = bp[bp$Limit<detached_threshold,]$Name
    }
    mylm <- ddply(d[d$group %in% (group_list),], 
                   c("group"), function(x) {
                model <- lm(Duration ~ Size, data = x)
                coef(model)
                })
    intercept_label = paste0(zone,"Intercept")
    size_label = paste0(zone,"Size")
    bp[,intercept_label] = 0
    bp[,size_label] = 0

    for(i in (mylm$group)) {
       bp[bp$Name == i,intercept_label] = mylm[mylm$group == i,"(Intercept)"]
       bp[bp$Name == i,size_label] = mylm[mylm$group == i,"Size"]
    }
    bp
  }

  display_lm <- function(d,remove_sync=FALSE,remove_detached=FALSE) {
    if(remove_sync) { 
       group_list = bp[bp$Limit<=detached_threshold,]$Name
    } else {
       group_list = bp$Name
    }
    if(remove_detached) {
       group_list = bp[bp$Limit<detached_threshold,]$Name
    }
    for(i in (1:length(group_list))) {
       print(paste0("----- ",bp[i,]$Name,"-----"))
       lim <- bp[i,]$Limit
       print(summary(lm(Duration ~ Size, data = d[d$group==bp[bp$Limit==lim,]$Name,])))
    }
  }

  df_send <- classify_messages(df_send,"OsBound")
  bp <- compute_lm(bp,df_send,"Os",remove_sync=T)
  display_lm(df_send,remove_sync=T)

  [1] "----- Small-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -5.148e-06 -5.866e-07 -1.344e-07  3.483e-07  1.046e-05 

  Coefficients:
	       Estimate Std. Error t value Pr(>|t|)    
  (Intercept) 8.930e-06  1.895e-08  471.19   <2e-16 ***
  Size        7.654e-10  4.761e-11   16.08   <2e-16 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 1.002e-06 on 3978 degrees of freedom
  Multiple R-squared: 0.06102,	Adjusted R-squared: 0.06078 
  F-statistic: 258.5 on 1 and 3978 DF,  p-value: < 2.2e-16 

  [1] "----- Medium1-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -9.536e-06 -1.129e-06 -3.070e-08  1.072e-06  2.606e-05 

  Coefficients:
	       Estimate Std. Error t value Pr(>|t|)    
  (Intercept) 1.397e-05  7.711e-08  181.14   <2e-16 ***
  Size        2.974e-10  5.617e-12   52.95   <2e-16 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 1.898e-06 on 1593 degrees of freedom
  Multiple R-squared: 0.6376,	Adjusted R-squared: 0.6374 
  F-statistic:  2803 on 1 and 1593 DF,  p-value: < 2.2e-16 

  [1] "----- Medium2-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -1.262e-05 -9.783e-07 -4.763e-07  5.691e-07  2.420e-05 

  Coefficients:
	       Estimate Std. Error t value Pr(>|t|)    
  (Intercept) 1.541e-05  9.010e-07   17.10   <2e-16 ***
  Size        2.441e-10  1.933e-11   12.63   <2e-16 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 2.622e-06 on 251 degrees of freedom
  Multiple R-squared: 0.3886,	Adjusted R-squared: 0.3862 
  F-statistic: 159.5 on 1 and 251 DF,  p-value: < 2.2e-16 

  [1] "----- Detached-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -1.727e-04 -9.724e-05  3.288e-05  6.266e-05  2.979e-04 

  Coefficients:
		Estimate Std. Error t value Pr(>|t|)    
  (Intercept)  2.420e-04  8.230e-06   29.41   <2e-16 ***
  Size        -2.652e-11  4.824e-11   -0.55    0.583    
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 9.811e-05 on 922 degrees of freedom
  Multiple R-squared: 0.0003276,	Adjusted R-squared: -0.0007567 
  F-statistic: 0.3021 on 1 and 922 DF,  p-value: 0.5827

Special treatment for detached mode as the Size parameter is not significant

    group = bp[bp$Limit==detached_threshold,]$Name

    mylm <- lm(Duration ~ 1, data = df_send[df_send$group==group,])
    c_detached = coef(mylm)
    bp[bp$Name == group,"OsIntercept"] = c_detached[[1]]
    bp[bp$Name == group,"OsSize"] = 0

  comm_function <- function(x,zone) {
        bp[x>=bp$LimitInf & x<bp$Limit,paste0(zone,"Intercept")] + 
    x * bp[x>=bp$LimitInf & x<bp$Limit,paste0(zone,"Size")]
  }

  fancy_plot <- function(d,zone) {
    d$values_test <- sapply(d$Size,function(x) {comm_function(x,zone)})
  
    pl <- ggplot(data=d, aes(x=Size,y=Duration,color=group))
    pl <- pl + geom_vline(xintercept=bp$Limit, colour="gray", linetype = "longdash")  + 
               annotate("text", x=bp$Limit, 
                        y=seq(.1*max(d$Duration),2*max(d$Duration),length.out=length(bp$Limit)),
                        label=bp$Name)
    pl <- pl + geom_point(alpha=.3)
    pl <- pl + geom_line(aes(x=Size,y=values_test), colour="black")
    pl <- pl + scale_x_log10(limits=c(1, max(d$Size))) + scale_y_log10()
    pl + ylab("MPI_Send duration (seconds)") + xlab("Message size (bytes)") + theme_bw() + scale_alpha(guide = "none")
  }
  fancy_plot(df_send[df_send$group!="outliers",],"Os")

  basic_plot(df_recv)

  df_recv <- classify_messages(df_recv,"OrBound")
  bp <- compute_lm(bp, df_recv,"Or",remove_detached=TRUE)
  display_lm(df_recv,remove_detached=TRUE)

  [1] "----- Small-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -1.167e-06 -3.148e-07 -1.014e-07  1.811e-07  1.134e-05 

  Coefficients:
	       Estimate Std. Error t value Pr(>|t|)    
  (Intercept) 8.140e-06  1.348e-08  603.72   <2e-16 ***
  Size        8.396e-10  3.389e-11   24.77   <2e-16 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 6.805e-07 on 3626 degrees of freedom
  Multiple R-squared: 0.1447,	Adjusted R-squared: 0.1445 
  F-statistic: 613.6 on 1 and 3626 DF,  p-value: < 2.2e-16 

  [1] "----- Medium1-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -2.945e-06 -6.824e-07 -2.118e-07  3.956e-07  2.432e-05 

  Coefficients:
	       Estimate Std. Error t value Pr(>|t|)    
  (Intercept) 1.270e-05  6.273e-08   202.5   <2e-16 ***
  Size        9.092e-10  4.973e-12   182.8   <2e-16 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 1.413e-06 on 1374 degrees of freedom
  Multiple R-squared: 0.9605,	Adjusted R-squared: 0.9605 
  F-statistic: 3.343e+04 on 1 and 1374 DF,  p-value: < 2.2e-16 

  [1] "----- Medium2-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -6.351e-06 -2.408e-06 -4.990e-07  1.274e-06  5.252e-05 

  Coefficients:
	       Estimate Std. Error t value Pr(>|t|)    
  (Intercept) 3.096e-05  2.048e-06   15.12   <2e-16 ***
  Size        6.956e-10  4.392e-11   15.84   <2e-16 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 5.682e-06 on 228 degrees of freedom
  Multiple R-squared: 0.5239,	Adjusted R-squared: 0.5218 
  F-statistic: 250.9 on 1 and 228 DF,  p-value: < 2.2e-16

  fancy_plot(df_recv,"Or")

Let's analyze the Ping Pong experiment. We assume it was done using a simple send+recv. Let's sum the times taken by the pair on node 0, let's forget node 1.

  basic_plot(df_pingpong)

  df_pingpong <- classify_messages(df_pingpong,"PingPongBound")
  bp <- compute_lm(bp, df_pingpong,"PingPong")
  display_lm(df_pingpong)

  [1] "----- Small-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -5.414e-05 -9.222e-06 -6.302e-06  9.010e-07  2.222e-04 

  Coefficients:
	       Estimate Std. Error t value Pr(>|t|)    
  (Intercept) 7.318e-05  5.476e-07  133.63   <2e-16 ***
  Size        4.074e-08  1.379e-09   29.54   <2e-16 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 2.725e-05 on 3521 degrees of freedom
  Multiple R-squared: 0.1986,	Adjusted R-squared: 0.1983 
  F-statistic: 872.4 on 1 and 3521 DF,  p-value: < 2.2e-16 

  [1] "----- Medium1-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -7.655e-05 -4.697e-05 -2.416e-05 -3.400e-06  1.546e-03 

  Coefficients:
	       Estimate Std. Error t value Pr(>|t|)    
  (Intercept) 1.777e-04  5.812e-06   30.57   <2e-16 ***
  Size        1.842e-08  4.234e-10   43.51   <2e-16 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 0.000136 on 1437 degrees of freedom
  Multiple R-squared: 0.5685,	Adjusted R-squared: 0.5682 
  F-statistic:  1893 on 1 and 1437 DF,  p-value: < 2.2e-16 

  [1] "----- Medium2-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -1.175e-04 -6.066e-05 -3.421e-05  3.739e-05  1.139e-03 

  Coefficients:
	       Estimate Std. Error t value Pr(>|t|)    
  (Intercept) 3.056e-04  4.443e-05   6.879 5.97e-11 ***
  Size        1.553e-08  9.502e-10  16.348  < 2e-16 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 0.0001219 on 224 degrees of freedom
  Multiple R-squared: 0.544,	Adjusted R-squared: 0.542 
  F-statistic: 267.3 on 1 and 224 DF,  p-value: < 2.2e-16 

  [1] "----- Detached-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -2.937e-04 -1.823e-04 -4.085e-05  1.142e-04  2.332e-03 

  Coefficients:
	       Estimate Std. Error t value Pr(>|t|)    
  (Intercept) 5.754e-04  2.449e-05   23.49   <2e-16 ***
  Size        1.673e-08  1.436e-10  116.57   <2e-16 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 0.0002784 on 838 degrees of freedom
  Multiple R-squared: 0.9419,	Adjusted R-squared: 0.9418 
  F-statistic: 1.359e+04 on 1 and 838 DF,  p-value: < 2.2e-16 

  [1] "----- Large-----"

  Call:
  lm(formula = Duration ~ Size, data = d[d$group == bp[bp$Limit == 
      lim, ]$Name, ])

  Residuals:
	 Min         1Q     Median         3Q        Max 
  -0.0004040 -0.0002220 -0.0000752  0.0000947  0.0031745 

  Coefficients:
	       Estimate Std. Error t value Pr(>|t|)    
  (Intercept) 4.632e-04  7.120e-05   6.506 1.99e-10 ***
  Size        1.721e-08  1.060e-10 162.253  < 2e-16 ***
  ---
  Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

  Residual standard error: 0.0004066 on 468 degrees of freedom
  Multiple R-squared: 0.9825,	Adjusted R-squared: 0.9825 
  F-statistic: 2.633e+04 on 1 and 468 DF,  p-value: < 2.2e-16

  fancy_plot(df_pingpong,"PingPong")

Since we ensured in the experiments that receiver is ready, we have pingpong = 2or+2transfer for small messages that are sent asynchronously. For large sizes, communications are synchronous, hence we have pingpong = 2transfer.

  ### lm of Or is 0 above async_threshold so we can safely substract
  bp$DelayIntercept <- (bp$PingPongIntercept-bp$OrIntercept)/2
  bp$DelaySize <- (bp$PingPongSize-bp$OrSize)/2

  df_pingpong$values_test2 <- sapply(df_pingpong$Size,
      function(x) {comm_function(x,"Delay")})

  df_pingpong$Duration2 = (df_pingpong$Duration - 
     sapply(df_pingpong$Size,function(x) {comm_function(x,"Or")}))/2

  pl <- ggplot(data=df_pingpong, aes(x=Size,y=Duration2,color=group))+geom_point(alpha=.2)
  pl <- pl + geom_vline(xintercept=c(limit_small,limit_medium,limit_mediump,limit_medium_large), colour="black", linetype = "longdash")
  pl + geom_line(aes(x=Size,y=values_test2), colour="black") +scale_x_log10()+scale_y_log10()

   a <- xmlNode("config", attrs = c(id="General"), os, or, bw, lat, as, de)
   saveXML(a, file="testXML.xml")

[1] "testXML.xml"

   cat "testXML.xml"

<?xml version="1.0"?>
<config id="General">
 <prop id="smpi/os" value="0:8.9300920419081e-06:7.65438202550106e-10;1420:1.39684254077781e-05:2.97409403415968e-10;32768:1.54082820250394e-05:2.44104034252286e-10;65536:0.000237866424242424:0;327680:0:0"/>
 <prop id="smpi/or" value="0:8.14025462333494e-06:8.3958813204998e-10;1420:1.26995184134793e-05:9.09218191293861e-10;32768:3.09570602567453e-05:6.95645307772806e-10;65536:0:0;327680:0:0"/>
 <prop id="smpi/bw_factor" value="0:0.400976530736138;1420:0.913555534273577;32768:1.07831886657594;65536:0.956083935262915;327680:0.929867998857892"/>
 <prop id="smpi/lat_factor" value="0:1.35489260823384;1420:3.43725032107889;32768:5.72164710873587;65536:11.9885319715471;327680:9.65041953605594"/>
 <prop id="smpi/async_small_thres" value="65536"/>
 <prop id="smpi/send_is_detached_thres" value="327680"/>
</config>

  desc=data.frame()
  desc=rbind(desc, ddply(bp,c("Name"), summarize, Name="smpi/os",Limit=Limit, desc=paste0(LimitInf,":",LogGP_OsIntercept,":",LogGP_OsSize)))
  desc=rbind(desc, ddply(bp,c("Name"), summarize, Name="smpi/or",Limit=Limit, desc=paste0(LimitInf,":",LogGP_OrIntercept,":",LogGP_OrSize)))
  desc=rbind(desc, ddply(bp,c("Name"), summarize, Name="smpi/bw_factor",Limit=Limit, desc=paste0(LimitInf,":",1/(LogGP_DelaySize*1.25E8))))
  desc=rbind(desc, ddply(bp,c("Name"), summarize, Name="smpi/lat_factor",Limit=Limit, desc=paste0(LimitInf,":",LogGP_DelayIntercept/2.4E-5)))

  desc <- desc[with(desc, order(Name,Limit)),]
  desc <- ddply(desc,c("Name"),summarize,label=paste(desc,collapse = ';'))

  as <- xmlNode("prop", attrs = c(id="smpi/async_small_thres", value="65536"))
  de <- xmlNode("prop", attrs = c(id="smpi/send_is_detached_thres", value="65536"))
  bw <- xmlNode("prop", attrs = c(id="smpi/bw_factor", value=desc[desc$Name=="smpi/bw_factor",]$label))
  lat <- xmlNode("prop", attrs = c(id="smpi/lat_factor", value=desc[desc$Name=="smpi/lat_factor",]$label))
  os <- xmlNode("prop", attrs = c(id="smpi/os", value=desc[desc$Name=="smpi/os",]$label))
  or <- xmlNode("prop", attrs = c(id="smpi/or", value=desc[desc$Name=="smpi/or",]$label))   

  a <- xmlNode("config", attrs = c(id="General"), os, or, bw, lat, as, de)
  saveXML(a, file="LogGPS.xml")

[1] "LogGPS.xml"

  cat "LogGPS.xml"

<?xml version="1.0"?>
<config id="General">
 <prop id="smpi/os" value="0:1.00232317408165e-05:4.15590748439781e-10;1420:1.00232317408165e-05:4.15590748439781e-10;32768:1.00232317408165e-05:4.15590748439781e-10;65536:1.00232317408165e-05:4.15590748439781e-10;327680:1.00232317408165e-05:4.15590748439781e-10"/>
 <prop id="smpi/or" value="0:9.00185524188329e-06:1.19998810064746e-09;1420:9.00185524188329e-06:1.19998810064746e-09;32768:9.00185524188329e-06:1.19998810064746e-09;65536:9.00185524188329e-06:1.19998810064746e-09;327680:9.00185524188329e-06:1.19998810064746e-09"/>
 <prop id="smpi/bw_factor" value="0:0.409556304333763;1420:0.988092528012222;32768:0.988092528012222;65536:0.988092528012222;327680:0.988092528012222"/>
 <prop id="smpi/lat_factor" value="0:1.87252265739663;1420:3.02824490687664;32768:3.02824490687664;65536:3.02824490687664;327680:3.02824490687664"/>
 <prop id="smpi/async_small_thres" value="65536"/>
 <prop id="smpi/send_is_detached_thres" value="65536"/>
</config>