DOWNLOAD MY Ph.D Thesis - UNAM

Chapter 4Simulation and analytical modelling pThen, the number of MCI frames required to transmit a data packet is Pk slots over themaximum number of reservation slots per MCI frame. Thus:⎧ Pkslot⎪when Pkslotmod MCImax_ slots− MCICSs= 0MCImax_ slots− MCICSsPk = ⎨(4.23)mci⎪ Pkslot+ 1 otherwise⎪⎩ MCImax_ slots− MCICSswhere MCI max_slots and MCI CSs correspond to the maximum number of upstream slotsdescribed per MCI frame and the minimum number of contention slots per MCI frame,respectively.By substituting X t1 , X t2 and X t3 from Equations 4.16, 4.17 and 4.21 respectively inEquation 4.15, the service time in an idle state now becomes:XidleMCIt= + MCI⋅ MCIt+ Pkmci⋅ MCIt= (0.5 + MCI+ Pkmci)2⋅ MCIt(4.24)The service time in a busy state (X busy ) is similar to X idle , but the only difference is thatnew packets, finding the system busy, spend a complete MCI frame looking for acontention slot in which to place a reservation request instead of MCI t /2. Thus, thecalculation for X busy is given by:Xbusy= MCI + X2+ X = (1 + + Pk ) ⋅ MCI(4.25)ttt3MCImcitUp to this point, we have calculated all the elements of the initial mean service time.Thus by substituting Equations 4.13, 4.14, 4.24 and 4.25 in Equation 4.12,calculated as:X ' is thenHence,λλX ' = (1 − ) ⋅ (0.5 + MCI+ Pkmci) ⋅ MCIt+ ⋅ (1 + MCI+ Pkmci) ⋅ MCIµµt⎛λ ⎞X ' = ⎜ Pkmci+ 0.5 + MCI+ ⎟ ⋅ MCI(4.26)t⎝2 ⋅ µ ⎠We can now derive the real mean service time ( X ) when the third case of service time(X 2 ) is considered. Since not all newcomer packets finding the system in idle state are4-26