Optimal Joint Offloading and Wireless Scheduling for Parallel Computing with Deadlines Weijian Xu† Xudong Qin* Bin Li* *Dept. of Electrical, Computer and Biomedical Engineering, University of Rhode Island, Rhode Island, USA †Information Engineering College, Jimei University, Xiamen, China
Real-time Mobile Applications Real-time video analysis Real-time language translation Low energy consumption Low latency requirements Intensive computation requirements
System Model User 1 User 2 ⋱ Access point User N Edge servers Mobile users
System Model (Cont ’) Each user 𝑜 has dynamic and heterogeneous computing demands 𝐿−1 𝑂 1 with strict 𝑈 time slots deadline. min limsup 𝐿 𝔽[𝑄 𝑜 [𝑙: (𝑙 + 1)]] 𝐿→∞ 𝑙=0 𝑜=1 ↓ 𝐵 𝑜 𝑙𝑈 packets 0 T slots s. t. 𝜇 𝑜 1 − 𝜍 𝑜 ≤ 𝜉 𝑜 , ∀𝑜, 𝑙, (𝑀) 𝑙𝑈 + 𝐵 𝑜 (𝐹) 𝑙𝑈 = 𝐵 𝑜 𝑙𝑈 , 𝐵 𝑜 ∀𝑜, 𝑙, where 𝔽 𝐵 𝑜 𝑙𝑈 = 𝜇 𝑜 , 𝜍 𝑜 is the maximal Local computation allowable drop rate for user 𝑜 , 𝜉 𝑜 is the total number of packets that can be (𝑀) 𝑙𝑈 processed in frame 𝑙 . 𝐵 𝑜 are the Transmission to edge server Drop packets packets that perform local computation and 𝐸 𝑜 [𝑙𝑈] (𝐹) 𝑙𝑈 are the transmission part. Mobile User 𝑜 𝐵 𝑜 Energy Consumption: 𝑄 𝑜 [𝑙: 𝑙 + 1 ] Time frame In time frame 𝑙 , 𝑙 + 1 𝜉 𝑜 packets can be processed
A Motivating Example Local-First Offloading and Scheduling (LFOS) Algorithm Edge-First Offloading and Scheduling (EFOS) Algorithm Remaining parts Arriving packets are Arriving packets are Remaining parts are transmitted to transmitted to edge processed at mobile are processed at edge server server first device first mobile device
A Motivating Example (Cont ’) 6 packets Policy User t=0 t=1 t=2 t=3 t=4 t=5 1 LFOS Access point 2 2 mobile users 1 Edge servers EFOS 2 1 System setup : 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, Better each user has 6 packets waiting to be processed. Choice 2 ❖ In each slot, a mobile device can process 1 packet with 7 watt energy consumption; ❖ In each slot, a mobile device can transmit 2 packets with 4 watt energy consumption; ❖ Only one user can transmit packet within one slot.
A Motivating Example (Cont ’) Packets remaining Policy User t=0 t=1 t=2 t=3 t=4 t=5 1 3, 11 LFOS Access point 2 5, 7 2 mobile users 1 3, 11 Edge servers EFOS 2 5, 7 1 4, 4 System setup : 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, Better each user has 6 packets waiting to be processed. Choice 2 ❖ In each slot, a mobile device can process 1 packet with 7 watt energy consumption; ❖ In each slot, a mobile device can transmit 2 packets with 4 watt energy consumption; Energy consumption ❖ Only one user can transmit packet within one slot.
A Motivating Example (Cont ’) Packets remaining Policy User t=0 t=1 t=2 t=3 t=4 t=5 1 3, 11 0, 11 LFOS Access point 2 5, 7 4, 7 2 mobile users 1 3, 11 0, 11 Edge servers EFOS 2 5, 7 4, 7 1 4, 4 2, 4 System setup : 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, Better each user has 6 packets waiting to be processed. Choice 2 ❖ In each slot, a mobile device can process 1 packet with 7 watt energy consumption; ❖ In each slot, a mobile device can transmit 2 packets with 4 watt energy consumption; Energy consumption ❖ Only one user can transmit packets within one slot.
A Motivating Example (Cont ’) Packets remaining Policy User t=0 t=1 t=2 t=3 t=4 t=5 1 3, 11 0, 11 LFOS Access point 2 5, 7 4, 7 1, 11 2 mobile users 1 3, 11 0, 11 Edge servers EFOS 2 5, 7 4, 7 1, 11 1 4, 4 2, 4 0, 4 System setup : 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, Better each user has 6 packets waiting to be processed. Choice 2 ❖ In each slot, a mobile device can process 1 packet with 7 watt energy consumption; ❖ In each slot, a mobile device can transmit 2 packets with 4 watt energy consumption; Energy consumption ❖ Only one user can transmit packet within one slot.
A Motivating Example (Cont ’) Packets remaining Policy User t=0 t=1 t=2 t=3 t=4 t=5 1 3, 11 0, 11 LFOS Access point 2 5, 7 4, 7 1, 11 0, 7 2 mobile users 1 3, 11 0, 11 Edge servers EFOS 2 5, 7 4, 7 1, 11 0, 4 1 4, 4 2, 4 0, 4 System setup : 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, Better each user has 6 packets waiting to be processed. Choice 2 4, 4 ❖ In each slot, a mobile device can process 1 packet with 7 watt energy consumption; ❖ In each slot, a mobile device can transmit 2 packets with 4 watt energy consumption; Energy consumption ❖ Only one user can transmit packet within one slot.
A Motivating Example (Cont ’) Packets remaining Policy User t=0 t=1 t=2 t=3 t=4 t=5 1 3, 11 0, 11 LFOS Access point 2 5, 7 4, 7 1, 11 0, 7 2 mobile users 1 3, 11 0, 11 Edge servers EFOS 2 5, 7 4, 7 1, 11 0, 4 1 4, 4 2, 4 0, 4 System setup : 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, Better each user has 6 packets waiting to be processed. Choice 2 4, 4 2, 4 ❖ In each slot, a mobile device can process 1 packet with 7 watt energy consumption; ❖ In each slot, a mobile device can transmit 2 packets with 4 watt energy consumption; Energy consumption ❖ Only one user can transmit packet within one slot.
A Motivating Example (Cont ’) Packets remaining Policy User t=0 t=1 t=2 t=3 t=4 t=5 1 3, 11 0, 11 LFOS Access point 2 5, 7 4, 7 1, 11 0, 7 2 mobile users 1 3, 11 0, 11 Edge servers EFOS 2 5, 7 4, 7 1, 11 0, 4 1 4, 4 2, 4 0, 4 System setup : 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, Better each user has 6 packets waiting to be processed. Choice 2 4, 4 2, 4 0, 4 ❖ In each slot, a mobile device can process 1 packet with 7 watt energy consumption; ❖ In each slot, a mobile device can transmit 2 packets with 4 watt energy consumption; Energy ❖ Only one user can transmit packet within one slot. consumption
A Motivating Example (Cont ’) Policy User t=0 t=1 t=2 t=3 t=4 t=5 1 3, 11 0, 11 LFOS 2 5, 7 4, 7 1, 11 0, 7 1 3, 11 0, 11 EFOS 2 5, 7 4, 7 1, 11 0, 4 Access point 1 4, 4 2, 4 0, 4 Better Choice 2 mobile users 2 4, 4 2, 4 0, 4 Edge servers System setup : 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, Policy LFOS EFOS Better choice each user has 6 packets waiting to be processed. Average Energy ❖ In each slot, a mobile device can process 1 packet with 4.5 4.25 2 consumption for 7 watt energy consumption; each user(watt) ❖ In each slot, a mobile device can transmit 2 packets with 4 watt energy consumption; A better choice can save energy consumption up to 55.6% ❖ Only one user can transmit packet within one slot. compared to LFOS.
Algorithm Design We introduce a virtual queue 𝑌 𝑜 [𝑙𝑈] to keep track of the amount of packets that are dropped . Virtual queue 𝑌 𝑜 [𝑙𝑈] Virtual queue arrival: Virtual queue service: 𝐸 𝑜 [𝑙𝑈] packets drop 𝐶 𝑜 [𝑙𝑈] service is generated, where 𝔽[𝐶 𝑜 𝑙𝑈 = 𝜍 𝑜 𝜇 𝑜 Virtual queue dynamics: + 𝑌 𝑜 𝐿 + 1 𝑈 = 𝑌 𝑜 𝑙𝑈 + 𝐸 𝑜 𝑙𝑈 − 𝐶 𝑜 𝑙𝑈 where 𝑦 + = max 𝑦, 0 for any real number 𝑦. Then the average drop rate of user 𝑜 meets the requirement if its virtual queue is stable (c.f. [1, Definition 2.2] ). [1] M. Neely, Stochastic network optimization with application to communication and queueing systems. Morgan & Claypool, 2010
Joint Offloading and Scheduling Algorithm Joint Offloading and Scheduling ( JOS) algorithm (𝑀) 𝑙𝑈 + σ 𝑜=1 (𝐹) [𝑙𝑈] , 𝑂 𝑂 σ 𝑜=1 max 𝐺 𝐺 Strongly coupled 𝑜 𝑜 where 𝑀 𝑙𝑈 (𝑀) 𝑙𝑈 ≜ 𝑌 𝑜 𝑙𝑈 min 𝐵 𝑜 𝑀 𝑙𝑈 , 𝑈𝜈 𝑜 − 𝑁𝑓 𝑜 𝑀 min 𝐵 𝑜 𝐺 , 𝑈 , 𝑜 𝜈 𝑜 Nonlinear ቄ 𝐹 𝑙𝑈 ≜ 𝑌 𝑜 𝑙𝑈 min{ 𝐵 𝑜 𝐹 [𝑙𝑈] , 𝐷 𝑜 𝑙𝑈 σ 𝑢=𝑙𝑈 𝑙+1 𝑈−1 𝑇 𝑜 𝑢 } − 𝑁𝑓 𝑜 (𝐹) σ 𝑢=𝑙𝑈 𝑙+1 𝑈−1 𝑇 𝑜 [𝑢] , 𝐺 𝑜 (𝐹) 𝑙𝑈 + 𝐵 𝑜 (𝑀) 𝑙𝑈 = 𝐵 𝑜 𝑙𝑈 . 𝑁 > 0 is some parameter, 𝐵 𝑜 Proposition 1 : The JOS algorithm with any 𝑁 > 0 achieves 𝑃 Τ 1 𝑁 close to the optimal energy consumption at the expense of the mean virtual queue-length growing with 𝑃(𝑁) .
Algorithm Implement Roadmap In JOS algorithm, the offloading decisions and wireless scheduling decisions are strongly coupled, which make Decoupled Joint Offloading and Scheduling it hard to implement ( DJOS ) algorithm Consider one time slot deadline setup, we build decoupled joint offloading and scheduling ( DJOS ) algorithm for the case with one time slot deadline. Wireless scheduling decisions Offloading decisions Based on the insight of one time slot DJOS, we developed DJOS for the general case.
Recommend
More recommend
