Effect of Mobile Phones on Life

Littles Theorem Littles Theorem (sometimes called Littles Law) is a statement of what was a folk theorem in operations research for many a(prenominal) years N = ? T where N is the random variable for the result of jobs or customers in a system, ? is the arrival rate at which jobs arrive, and T is the random variable for the time a job spends in the system (all of this assuming steady-state). What is remarkable about Littles Theorem is that it applies to any system, regardless of the arrival time process or what the system looks like inside.Proof Define the following ? ( t ) ? number of arrivals in the interval (0,t ) ? ( t ) ? number of departures in the interval (0,t ) N ( t ) ? number of jobs in the system at time t = ? (t ) ? ?( t ) ? ( t ) ? accumulated customer seconds in (0,t ) These functions are graphically shown in the following think The shaded area between the arrival and departure curves is ? (t ) . ? t = arrival rate over the interval (0,t ) ? (t ) t Elec 428 Little s Theorem N t = average of jobs during the interval (0,t ) = ? (t) t Tt = average time a job spends in the system in (0,t ) = ? (t) ? (t) ? ? ( t ) = Tt? ( t ) T ? (t ) ? Nt = t = ? t Tt t Assume that the following limits exist lim ? t = ? t ? lim Tt = T t ? Then lim N t = N t ? also exists and is given by N = ? T . Keywords Littles Law Littles Theorem Steady state Page 2 of 2