WEB SERVER PERFORMANCE MODELING AND ANALYSIS Cao Zhichao, Huang Chen and Lou Xiao
CONTENT <ul><li>Problem focus </li></ul><ul><li>Method and purpose </li></ul><ul><li>Calculation of parameters in two mode...
PROBLEM FOCUS <ul><li>Facing the growing visitors year after year from the website, the company has the problems of: </li>...
PURPOSE AND METHOD  <ul><li>Analyze the data from the log files provided realistically by the company </li></ul><ul><li>Im...
CALCULATION OF SOME PARAMETERS IN M/M/1 MODELS <ul><li>λ  (arrival rate) </li></ul><ul><ul><li>total number of arrivals(wh...
CALCULATION OF SOME PARAMETERS IN M/M/1 MODELS CON’D <ul><li>L (max number of places in the system) </li></ul><ul><ul><li>...
CALCULATION OF SOME PARAMETERS IN M/M/1 MODELS CON’D <ul><li>N  system (average time in the system) </li></ul><ul><ul><li>...
CALCULATION OF SOME PARAMETERS IN IPP/M/1 MODELS <ul><li>α and β (two states in IPP model) </li></ul><ul><ul><li>In IPP mo...
CALCULATION OF SOME PARAMETERS IN IPP/M/1 MODELS <ul><li>N  system </li></ul><ul><ul><li>It is difficult to calculate N wi...
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Web Server Performance Modeling And Analysis

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Web Server Performance Modeling And Analysis

  1. 1. WEB SERVER PERFORMANCE MODELING AND ANALYSIS Cao Zhichao, Huang Chen and Lou Xiao
  2. 2. CONTENT <ul><li>Problem focus </li></ul><ul><li>Method and purpose </li></ul><ul><li>Calculation of parameters in two models </li></ul><ul><li>M/M/1/L vs. IPP/M/1/L </li></ul><ul><li>Suggestions and propose </li></ul>
  3. 3. PROBLEM FOCUS <ul><li>Facing the growing visitors year after year from the website, the company has the problems of: </li></ul><ul><ul><li>Long waiting time (response time) </li></ul></ul><ul><ul><li>High rejection rate (blocking probability) </li></ul></ul>
  4. 4. PURPOSE AND METHOD <ul><li>Analyze the data from the log files provided realistically by the company </li></ul><ul><li>Implement the distinct queuing system modeling (M/M/1 vs. IPP/M/1) </li></ul><ul><li>Compare the effects by the different models </li></ul><ul><li>Suggest the feasible and effective modification to the current server </li></ul><ul><li>All above for fulfilling the requirement of 20% increasingly per year on the high visiting rate </li></ul>
  5. 5. CALCULATION OF SOME PARAMETERS IN M/M/1 MODELS <ul><li>λ (arrival rate) </li></ul><ul><ul><li>total number of arrivals(which is the number of rows in one log file) / total time period. </li></ul></ul><ul><li>λ eff (effective arrival rate) </li></ul><ul><ul><li>total number of arrivals - number of blocks) / total time period. </li></ul></ul>
  6. 6. CALCULATION OF SOME PARAMETERS IN M/M/1 MODELS CON’D <ul><li>L (max number of places in the system) </li></ul><ul><ul><li>L is the maximum number of places in the system at certain moment. This is obtained by picking a rejected customer and finding number of customers in the system when this customer arrived. </li></ul></ul><ul><li>μ (service rate) </li></ul><ul><ul><li>According to Little's theorem, ρ c = λ eff /μ, we can get the value of µ. </li></ul></ul>
  7. 7. CALCULATION OF SOME PARAMETERS IN M/M/1 MODELS CON’D <ul><li>N system (average time in the system) </li></ul><ul><ul><li>Given λ and μ , we can get ρ , and we have 201 places and can easily theoretically calculate the value of N according to the following equation : </li></ul></ul>
  8. 8. CALCULATION OF SOME PARAMETERS IN IPP/M/1 MODELS <ul><li>α and β (two states in IPP model) </li></ul><ul><ul><li>In IPP model, the time between arrivals has the following Laplace transform: </li></ul></ul><ul><ul><li>We firstly use formula </li></ul></ul><ul><ul><li>To get the value of E[x] </li></ul></ul><ul><ul><li>& its second moment; </li></ul></ul><ul><ul><li>And then use: </li></ul></ul><ul><ul><li>To get the α and β </li></ul></ul>
  9. 9. CALCULATION OF SOME PARAMETERS IN IPP/M/1 MODELS <ul><li>N system </li></ul><ul><ul><li>It is difficult to calculate N with the theoretical way, so here we start up to simulate IPP/M/1 model in mat lab to calculate it. </li></ul></ul><ul><ul><li>Three events in this simulation: </li></ul></ul><ul><ul><ul><li>Arrival Customers; </li></ul></ul></ul><ul><ul><ul><li>Empty system ; </li></ul></ul></ul><ul><ul><ul><li>Process in the system. </li></ul></ul></ul>

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