Shanghai Jiao Tong University RESERVATION SYSTEMS,PRIORITY QUEUEING AND SYSTEM STABILITY Weigiang Sun Communication Networks
Weiqiang Sun Communication Networks RESERVATION SYSTEMS, PRIORITY QUEUEING AND SYSTEM STABILITY Shanghai Jiao Tong University
Reservation systems Reservation systems Single server/channel shared by multiple users Only one user can use the channel at a time Need to coordinate between users 。Polling station Polls the users to see if they have anything to send One cycle R1 D1 R2 D2 R3 D3 R1 D1 R2 D2 Transmission interval Reservation interval,no transmission Weigiang Sun Communication Networks
Weiqiang Sun Communication Networks Reservation systems • Reservation systems – Single server/channel shared by multiple users – Only one user can use the channel at a time – Need to coordinate between users • Polling station – Polls the users to see if they have anything to send 2 R1 D1 R2 D2 R3 D3 R1 D1 R2 D2 Reservation interval, no transmission Transmission interval One cycle
Types of polling systems ·Exhaustive system Can send data arrives prior to the end of data interval Gated system Can send data arrives prior to reservation interval o Partially gated system Can send data arrives prior to data interval Limited service system Only one (k)packets can be sent in one data interval R1 D1 R2 D2 R3 D3 R1 D1 R2 D2 Gated system→ —Exhaustive system Partially gated system Weigiang Sun Communication Networks 3
Weiqiang Sun Communication Networks Types of polling systems • Exhaustive system – Can send data arrives prior to the end of data interval • Gated system – Can send data arrives prior to reservation interval • Partially gated system – Can send data arrives prior to data interval • Limited service system – Only one (k) packets can be sent in one data interval 3 R1 D1 R2 D2 R3 D3 R1 D1 R2 D2 Gated system Exhaustive system Partially gated system
Single user exhaustive system R D R D R D R D R D Customer i arrives ©X Xi-1 X-2 Xi-3 W Assume reservation intervals are i.i.d Identical to M/G/1 with vacations x2,2 W= Vacation period reservation period 2(1-p)'2V AX2 A If V=A (constant),then W= 2(1-p) 2 Weigiang Sun Communication Networks 4
Weiqiang Sun Communication Networks Single user exhaustive system • Assume reservation intervals are i.i.d • Identical to M/G/1 with vacations – Vacation period = reservation period 4 R D R D R D R D R D Xi Xi-1 Xi-2 Xi-3 Customer i arrives Wi Ri 2 2 2 1 2 X V W V If V=A (constant), then 2 2 1 2 X A W
Single user gated system R D R D R D R D R D Customer i arrives @X, X-2 Xi-3 亚 W R W,=R+∑X,+V Weigiang Sun Communication Networks 5
Weiqiang Sun Communication Networks Single user gated system 5 R D R D R D R D R D Xi Xi-2 Vi Xi-3 Customer i arrives Wi Vi-1 Ri W R X V i i i i