How to count the number of concurrent users using time interval data?

Question

I have a data set representing data from a log file which shows users and machine taking a connection for a server. I have a connection start time (variable start) and end time (variable end) in the dataset:

tdata <- structure(list(username = structure(c(9L, 6L, 7L, 5L, 3L, 2L, 
4L, 8L, 1L, 4L), .Label = c("ESSAA", "HBRTE", "HPAIUS", 
"KOLA", "MAITAEN", "MARKEA", "MIAINN", "MSALA", 
"PAREDT"), class = "factor"), machine = structure(c(3L, 2L, 
4L, 8L, 1L, 5L, 9L, 6L, 7L, 9L), .Label = c("D5785.domain.com", 
"D5874.domain.com", "D5927.domain.com", "D6000.domain.com", 
"D6092.domain.com", "D6147.domain.com", "D6142.domain.com", 
"D6169.domain.com", "D6194.domain.com"), class = "factor"), 
    start = structure(c(1322672567, 1322687984, 1322465646, 1322696883, 
    1322695042, 1322697073, 1322697547, 1322692794, 1322697694, 
    1322700934), tzone = "", class = c("POSIXct", "POSIXt")), 
    end = structure(c(1322693766, 1322695797, 1322696945, 1322697004, 
    1322697284, 1322697303, 1322697781, 1322700307, 1322700667, 
    1322701224), tzone = "", class = c("POSIXct", "POSIXt"))), .Names = c("username", 
"machine", "start", "end"), row.names = c(NA, 10L), class = "data.frame")

> tdata
   username          machine               start                 end
1    PAREDT D5927.domain.com 2011-11-30 19:02:47 2011-12-01 00:56:06
2    MARKEA D5874.domain.com 2011-11-30 23:19:44 2011-12-01 01:29:57
3    MIAINN D6000.domain.com 2011-11-28 09:34:06 2011-12-01 01:49:05
4   MAITAEN D6169.domain.com 2011-12-01 01:48:03 2011-12-01 01:50:04
5    HPAIUS D5785.domain.com 2011-12-01 01:17:22 2011-12-01 01:54:44
6     HBRTE D6092.domain.com 2011-12-01 01:51:13 2011-12-01 01:55:03
7      KOLA D6194.domain.com 2011-12-01 01:59:07 2011-12-01 02:03:01
8     MSALA D6147.domain.com 2011-12-01 00:39:54 2011-12-01 02:45:07
9     ESSAA D6142.domain.com 2011-12-01 02:01:34 2011-12-01 02:51:07
10     KOLA D6194.domain.com 2011-12-01 02:55:34 2011-12-01 03:00:24
>

Now I would like to calculate the number of concurrent users for each minute using start and end times from the tdata dataset. I got this far:

#create dataset containing each minute from tdata
start.min <- min(tdata$start, na.rm=T)
end.max <- max(tdata$end, na.rm=T)
tinterval <- seq.POSIXt(start.min, end.max, by = "mins")

Any ideas how to proceed with the calculation?

Answer 1

Here is an example

n <- sapply(tinterval, function(tt) sum(tdata$start <= tt & tt <= tdata$end))

then

@> tail(data.frame(tinterval, n))
               tinterval n
3922 2011-12-01 09:55:06 0
3923 2011-12-01 09:56:06 1
3924 2011-12-01 09:57:06 1
3925 2011-12-01 09:58:06 1
3926 2011-12-01 09:59:06 1
3927 2011-12-01 10:00:06 1
@> plot(tinterval, n, type = "l")

quite slow though...

Answer 2

Just for kicks, here's an xts solution:

library(xts)
# create an empty xts object with the minute timestamps we're interested in
out <- xts(,align.time(tinterval,60))
# loop over each user
for(i in 1:NROW(tdata)) {
  # paste the start / end times into an xts-style range
  timeRange <- paste(format(tdata[i,c("start","end")]),collapse="/")
  # add the minute "by parameter" for timeBasedSeq
  timeRange <- paste(timeRange,"M",sep="/")
  # create the by-minute sequence and align to minutes to match "out"
  timeSeq <- align.time(timeBasedSeq(timeRange),60)
  # create xts object with "1" entries for times between start and end
  temp <- xts(rep(1,length(timeSeq)),timeSeq)
  # merge temp with out and fill non-matching timestamps with "0"
  out <- merge(out, temp, fill=0)
}
# add column names (if necessary)
colnames(out) <- tdata[,1]
# sum across rows (need xts constructor because rowSums returns a matrix)
counts <- xts(rowSums(out),index(out))