A measurement of the traffic generated by the packet source indicates that the average traffic is λ [packets/s] and maximum traffic is σ [packets/s]. The classic exponential distribution is not appropriate for modeling such a source of traffic, because the exponential distribution contains only one parameter (and two parameters were measured).To model such a source of motion, you can use the shifted exponential distribution which is described by two parameters ( γ , δ &gt; 0): f ( τ ) = { 0 τ &lt; d γ e − γ ( τ − d ) τ ≥ d Random variable τ is the time interval between successive packets.1. Draw a distribution graph (1). What is the relationship between the maximum traffic and δ, for the distribution (#)?2. Designate a mean value of the distribution (#).3. Based on measurements of traffic sources ( λ , σ ) select firstly δ parameter for distribution (#), then γ parameter for distribution (#).

Question

A measurement of the traffic generated by the packet source indicates that the average traffic is   λ [packets/s] and maximum traffic is   σ [packets/s]. The classic exponential distribution is not appropriate for modeling such a source of traffic, because the exponential distribution contains only one parameter (and two parameters were measured).To model such a source of motion, you can use the shifted exponential distribution which is described by two parameters (  γ  ,  δ  &amp;gt;  0):  f  (  τ  )  =      {                            0                          τ          &amp;lt;          d                                      γ                      e                          −              γ              (              τ              −              d              )                                                τ          ≥          d                        Random variable   τ is the time interval between successive packets.1. Draw a distribution graph (1). What is the relationship between the maximum traffic and   δ, for the distribution (#)?2. Designate a mean value of the distribution (#).3. Based on measurements of traffic sources   (  λ  ,  σ  ) select firstly   δ parameter for distribution (#), then   γ parameter for distribution (#).

Alec Blake · Accepted Answer

Part 1 is simple. If   δ is the minimum interarrival time for consecutive packets, where time is measured in seconds, then at most   1      /    δ packets can arrive in one second. For instance, if   δ  =  0.01 seconds, meaning that we are assured that the time between packets is at least 0.01 seconds, then the most packets we can observe in one second is 1/0.01=100 packets, and this is   σ. So  σ  δ  =  1.For Part 3, use what you know from Parts 1 and 2 to establish a relationship between   λ and   γ. The average traffic intensity   λ is simply the average you found in Part 2. Solve for   γ in terms of   λ and   σ.