132B_1_Sec08_Info_Stream_Traffic_Proc_090710A

132B_1_Sec08_Info_Stream_Traffic_Proc_090710A - Information...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Information Streams and Traffic Processes Professor Izhak Rubin Electrical Engineering Department UCLA © 2010-2011 by Izhak Rubin
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
(c) Prof. Izhak Rubin 2 Arrival Point Processes (1) z Messages arrive at the system in accordance with a stochastic point process : where A n denotes the arrival time of n th message, n 1. We generally set A 0 =0. z Associated with the arrival process A is the arrival counting process . where N t N(t) denotes the arrival count at t, expressing the number of messages arriving at the system during (0, t]. {} (1) , 1 . . , 1 , 1 p w A A n A A n n n > = + { } (2) , 0 , 0 , 0 = = N t N N t N(t) t A 0 A 1 A 2 A 3 1 2 0 T 2 T 3 T 1
Background image of page 2
(c) Prof. Izhak Rubin 3 Inter-Arrival Times and Renewal Point Processes The inter-arrival times are denoted as The arrival process A is typically assumed to be a Renewal point process , under which {T n , n 1} is a sequence of independent identically distributed (i.i.d.) random variables. Such a process is statistically characterized by the inter-arrival time distribution We set A(t) = 0, for t 0. (3) . 1 , 1 = n A A T n n n () ( ) (4) . t T P t A = t A 0 A 1 A 2 A 3 1 2 0 N(t) T 2 T 3 T 1 A 4
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
(c) Prof. Izhak Rubin 4 Arrival Processes (2) z The mean inter-arrival time is denoted as z The message arrival intensity (or rate) is given by z The arrival process is said to be a continuous-time arrival point process if A(t) is a continuous distribution having the probability density function a(t) = dA(t)/dt, t 0. z The arrival process is said to be a discrete-time arrival point process if A(t) is a discrete distribution, so that arrivals can occur only at times {t k = k σ +t 0 , k=0,1,2,…, }. z Slot duration = σ . We normalize the slot time, setting σ = 1. For a discrete-time arrival process, inter-arrival times are measured in [slots], and the inter-arrival time distribution is denoted as ( ) ) 5 ( . T E = α ) 6 ( . 1 λ = ( ) ( ) (7) . 1 , = = j j t j T P n
Background image of page 4
(c) Prof. Izhak Rubin 5 Arrival Processes (3) Fig. 1. Realizations of (a) continuous-time and (b) discrete-time stochastic point processes
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
(c) Prof. Izhak Rubin 6 Arrival Processes (4) z
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 22

132B_1_Sec08_Info_Stream_Traffic_Proc_090710A - Information...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online