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Simulation Tutorial By Bing Wang Assistant professor, CSE Department, University of Connecticut Web site Network Simulation Motivation: learn fundamentals of evaluating network performance via simulation Overview: fundamentals of discrete event simulation analyzing simulation outputs ns-2 simulation The evaluation spectrum simulation numerical models prototype emulation operational system What is simulation? system boundary exogenous inputs to system (the environment) system under study (has deterministic rules governing its behavior) “real” life observer program boundary pseudo random inputs to system (models environment) computer program simulates deterministic rules governing behavior observer “simulated” life Why Simulation? goal: study system performance, operation real-system not available, is complex/costly or dangerous (eg: space simulations, flight simulations) quickly evaluate design alternatives (eg: different system configurations) evaluate complex functions for which closed form formulas or numerical techniques not available Simulation: advantages/drawbacks advantages: drawbacks/dangers: Programming a simulation What ‘s in a simulation program? simulated time: internal (to simulation program) variable that keeps track of simulated time system “state”: variables maintained by simulation program define system “state” e.g., may track number (possibly order) of packets in queue, current value of retransmission timer events: points in time when system changes state each event has associated event time • e.g., arrival of packet to queue, departure from queue • precisely at these points in time that simulation must take action (change state and may cause new future events) model for time between events (probabilistic) caused by external environment Discrete Event Simulation simulation program maintains and updates list of future events: event list simulator structure: Need: well defined set of events for each event: simulated system action, updating of event list initialize event list get next (nearest future) event from event list time = event time process event (change state values, add/delete future events from event list update statistics n done? y Simulation: example packets arrive (avg. interrarrival time: 1/ l) to router (avg. execution time 1/m) with two outgoing links arriving packet joins link i with probability fi m1 l m2 state of system: size of each queue system events: job arrivals service time completions define performance measure to be gathered Simulation: example l m1 m2 Simulator actions on arrival event choose a link if link idle {place pkt in service, determine service time (random number drawn from service time distribution) add future event onto event list for pkt transfer completion, set number of pkts in queue to 1} if buffer full {increment # dropped packets, ignore arrival} else increment number in queue where queued create event for next arrival (generate interarrival time) stick event on event list Simulation: example l m1 m2 Simulator actions on departure event remove event, update simulation time, update performance statistics decrement counter of number of pkts in queue If (number of jobs in queue > 0) put next pkt into service – schedule completion event (generate service time for put) Gathering Performance Statistics Ni avg delay at queue i: record Dij : delay of customer j at queue i. Let Ni be # customers passing through queue i throughput at queue i, i = average queue length at i: Ti Ni total simulated time N i iTi Little’s Law D j 1 Ni ij Analyzing Output Results Each time we run a simulation, (using different random number streams), we will get different output results! distribution of random numbers to be used during simulation (interarrival, service times) random number sequence 1 input simulation output output results 1 random number sequence 2 input simulation output output results 2 random number sequence M input simulation output output results M …… …… …… Analyzing Output Results l m1 m2 W2,n: delay of nth departing customer from queue 2 Analyzing Output Results l m1 m2 each run shows variation in customer delay one run different from next statistical characterization of delay must be made expected delay of n-th customer behavior as n approaches infinity average of n customers Transient Behavior simulation outputs that depend on initial condition (i.e., output value changes when initial conditions change) are called transient characteristics “early” part of simulation later part of simulation less dependent on initial conditions l m1 m2 Effect of initial conditions histogram of delay of 20th customer, given initially empty (1000 runs) histogram of delay of 20th customer, given non-empty conditions (1000 runs) Simulation: example packets arrive (avg. interrarrival time: 1/ l) to router (avg. execution time 1/m) with two outgoing links arriving packet joins link i with probability fi l m1 m2 Steady state behavior output results may converge to limiting “steady state” value if simulation run “long enough” avg delay of packets [n, n+10] avg of 5 simulations discard statistics gathered during transient phase, e.g., ignore first n0 measurements of delay at queue 2 Ni Ti Dij j n0 N i n0 pick n0 so statistic is “approximately the same” for different random number streams and remains same as n increases Example: Random Waypoint Model Simplest random waypoint model: mobile picks next waypoint Mn uniformly in area, independent of past and present mobile picks next speed Vn uniformly in [vmin; vmax] independent of past and present mobile moves towards Mn at constant speed Vn Mn+1 Mn Issue with RWP Model: Decay Distributions of node speed, position, Speed (m/s) distances, etc change with time 100 users average 1 user Time (s) Confidence Intervals run simulation: get estimate X1 as estimate of performance metrics of interest repeat simulation M times (each with new set of random numbers), get X2, … XM – all different! which of X1, … XM is “right”? intuitively, average of M samples should be “better” than choosing any one of M samples M X X j 1 M j How “confident” are we in X? Confidence Intervals cannot get perfect estimate of true mean, m, with finite # samples look for bounds: find c1 and c2 such that: Probability(c1 < m < c2) = 1 – a [c1,c2]: confidence interval 100(1-a): confidence level Confidence Intervals: Central Limit Thm Central Limit Theorem: If samples X1, … XM independent and from same population with population mean m and standard deviation s, then M sample mean: X X j 1 j M is approximately normally distributed with mean u and standard deviation s M Confidence Intervals .. more don’t know population standard deviation; estimate it using sample (observed) standard deviation: sX 2 1 M 2 ( X X ) m M 1 m 1 X , s X we find upper and lower tails of normal distributions containing a100% of mass given 2 Confidence Intervals .. the recipe Given samples X1, …, XM, (e.g., having repeated simulation M times), compute M X sX2 X j 1 j M 1 M 2 ( X X ) m M 1 m 1 1.96s X 95% confidence interval: X M Interpretation of Confidence Interval If we calculate confidence intervals as in recipe, 95% of confidence intervals thus computed will contain true (unknown) population mean. Generating confidence intervals for steady state measures independent replications with deletions method of batch means autoregressive method regenerative method Independent replications 1. generate n independent replications with m samples, remove first l0 samples from each to obtain X 1 (m, l0 ), , X n (m, l0 ) 2. calculate sample mean and variance from X i (m, l0 ) 3. use t-distribution to compute confidence intervals 4. can combine with sequential stopping rule to obtain confidence interval of specified width. 0ther methods batch means: take single run, delete first l0 observations, divide remainder into n groups and obtain Xi for i-th, i = 1,…,n follow procedure for independent replications complication due to nonindependence of Xis potential efficiency due to deletion of only l0 observation autoregressive method: spectrum analysis: based on study of correlation of observations regenerative method: applicable to systems with regeneration points regeneration point future independent of past can construct observations for intervals between regeneration points that will be iid use of CLT provides confidence intervals Comparing two different systems Example: want to compare mean response times of two queues where arrival process remains unchanged but speed of servers are different. run each system n times (n sufficiently large) to get {X1,j} and {X2,j} and take Zj = (X1,j ,X2,j) as the observations to determine confidence intervals for method of common random number using the same streams to generate rvs for j-th runs of both systems usually results in smaller sample variance of {Zj} ns-2, the network simulator discrete event simulator modeling network protocols wired, wireless, satellite TCP, UDP, multicast, unicast web, telnet, ftp ad hoc, sensor nets infrastructure: stats, tracing, error models, etc. prepackaged protocols and modules, or create your own Our goal: flavor of ns: simple example, modification, execution and trace analysis “ns” components ns, the simulator itself (this is all we’ll have time for) nam, the Network AniMator visualize ns (or other) output GUI input simple ns scenarios pre-processing: traffic and topology generators post-processing: simple trace analysis, often in Awk, Perl, or Tcl tutorial: http://www.isi.edu/nsnam/ns/tutorial/index.html ns by example: http://nile.wpi.edu/NS/