Optimal Joint Offloading and Wireless Scheduling for Parallel - - PowerPoint PPT Presentation
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
Xudong Qin* Weijian Xu† 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 video analysis
Low latency requirements Low energy consumption Intensive computation requirements
Real-time language translation
Mobile users Access point Edge servers
User 1 User 2 User N
min limsup
𝐿→∞
1 𝐿
𝑙=0 𝐿−1
𝑜=1 𝑂
𝔽[𝑄
𝑜[𝑙: (𝑙 + 1)]]
𝜇𝑜 1 − 𝜍𝑜 ≤ 𝜉𝑜, ∀𝑜, 𝑙, 𝐵𝑜
(𝑀) 𝑙𝑈 + 𝐵𝑜 (𝐹) 𝑙𝑈 = 𝐵𝑜 𝑙𝑈 ,
∀𝑜, 𝑙,
where 𝔽 𝐵𝑜 𝑙𝑈 = 𝜇𝑜, 𝜍𝑜 is the maximal allowable drop rate for user 𝑜, 𝜉𝑜 is the total number
packets that can be processed in frame 𝑙. 𝐵𝑜
(𝑀) 𝑙𝑈
are the packets that perform local computation and 𝐵𝑜
(𝐹) 𝑙𝑈 are the transmission part.
Each user 𝑜 has dynamic and heterogeneous computing demands with strict 𝑈 time slots deadline.
Local computation Transmission to edge server Drop packets 𝐸𝑜 [𝑙𝑈] In time frame 𝑙, 𝜉𝑜 packets can be processed
T slots
Mobile User 𝑜
↓ 𝐵𝑜 𝑙𝑈 packets
Energy Consumption: 𝑄
𝑜[𝑙: 𝑙 + 1 ]
Time frame 𝑙 + 1
Local-First Offloading and Scheduling (LFOS) Algorithm
Arriving packets are processed at mobile device first Remaining parts are transmitted to edge server
Edge-First Offloading and Scheduling (EFOS) Algorithm
Arriving packets are transmitted to edge server first Remaining parts are processed at mobile device
Policy User t=0 t=1 t=2 t=3 t=4 t=5 LFOS
1 2
EFOS
1 2
Better Choice
1 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.
2 mobile users Access point Edge servers
System setup: 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, each user has 6 packets waiting to be processed.
6 packets
Policy User t=0 t=1 t=2 t=3 t=4 t=5 LFOS
1 3, 11 2 5, 7
EFOS
1 3, 11 2 5, 7
Better Choice
1 4, 4 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.
2 mobile users Access point Edge servers
System setup: 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, each user has 6 packets waiting to be processed.
Packets remaining Energy consumption
Policy User t=0 t=1 t=2 t=3 t=4 t=5 LFOS
1 3, 11 0, 11 2 5, 7 4, 7
EFOS
1 3, 11 0, 11 2 5, 7 4, 7
Better Choice
1 4, 4 2, 4 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 packets within one slot.
2 mobile users Access point Edge servers
System setup: 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, each user has 6 packets waiting to be processed.
Packets remaining Energy consumption
Policy User t=0 t=1 t=2 t=3 t=4 t=5 LFOS
1 3, 11 0, 11 2 5, 7 4, 7 1, 11
EFOS
1 3, 11 0, 11 2 5, 7 4, 7 1, 11
Better Choice
1 4, 4 2, 4 0, 4 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.
2 mobile users Access point Edge servers
System setup: 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, each user has 6 packets waiting to be processed.
Packets remaining Energy consumption
Policy User t=0 t=1 t=2 t=3 t=4 t=5 LFOS
1 3, 11 0, 11 2 5, 7 4, 7 1, 11 0, 7
EFOS
1 3, 11 0, 11 2 5, 7 4, 7 1, 11 0, 4
Better Choice
1 4, 4 2, 4 0, 4 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; ❖ Only one user can transmit packet within one slot.
2 mobile users Access point Edge servers
System setup: 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, each user has 6 packets waiting to be processed.
Energy consumption Packets remaining
Policy User t=0 t=1 t=2 t=3 t=4 t=5 LFOS
1 3, 11 0, 11 2 5, 7 4, 7 1, 11 0, 7
EFOS
1 3, 11 0, 11 2 5, 7 4, 7 1, 11 0, 4
Better Choice
1 4, 4 2, 4 0, 4 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; ❖ Only one user can transmit packet within one slot.
2 mobile users Access point Edge servers
System setup: 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, each user has 6 packets waiting to be processed.
Packets remaining Energy consumption
Policy User t=0 t=1 t=2 t=3 t=4 t=5 LFOS
1 3, 11 0, 11 2 5, 7 4, 7 1, 11 0, 7
EFOS
1 3, 11 0, 11 2 5, 7 4, 7 1, 11 0, 4
Better Choice
1 4, 4 2, 4 0, 4 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; ❖ Only one user can transmit packet within one slot.
2 mobile users Access point Edge servers
System setup: 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, each user has 6 packets waiting to be processed.
Energy consumption Packets remaining
Policy User t=0 t=1 t=2 t=3 t=4 t=5 LFOS
1 3, 11 0, 11 2 5, 7 4, 7 1, 11 0, 7
EFOS
1 3, 11 0, 11 2 5, 7 4, 7 1, 11 0, 4
Better Choice
1 4, 4 2, 4 0, 4 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; ❖ Only one user can transmit packet within one slot.
2 mobile users Access point Edge servers
System setup: 𝑈 = 6 slots, 𝑂 = 2 users, at time 𝑢 = 0, each user has 6 packets waiting to be processed.
Policy LFOS EFOS Better choice Average Energy consumption for each user(watt)
A better choice can save energy consumption up to 55.6% compared to LFOS.
We introduce a virtual queue 𝑌𝑜[𝑙𝑈] to keep track of the amount of packets that are dropped.
Virtual queue arrival: 𝐸𝑜[𝑙𝑈] packets drop
Virtual queue 𝑌𝑜[𝑙𝑈]
Virtual queue service: 𝐶𝑜[𝑙𝑈] service is generated, where 𝔽[𝐶𝑜 𝑙𝑈 = 𝜍𝑜𝜇𝑜
Virtual queue dynamics: 𝑌𝑜 𝐿 + 1 𝑈 = 𝑌𝑜 𝑙𝑈 + 𝐸𝑜 𝑙𝑈 − 𝐶𝑜 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 (JOS) algorithm max σ𝑜=1
𝑂
𝐺
𝑜 (𝑀) 𝑙𝑈 + σ𝑜=1 𝑂
𝐺
𝑜 (𝐹)[𝑙𝑈],
where 𝐺
𝑜 (𝑀) 𝑙𝑈 ≜ 𝑌𝑜 𝑙𝑈 min 𝐵𝑜 𝑀 𝑙𝑈 , 𝑈𝜈𝑜 − 𝑁𝑓𝑜 𝑀 min 𝐵𝑜
𝑀 𝑙𝑈
𝜈𝑜
, 𝑈 , 𝐺
𝑜 𝐹 𝑙𝑈 ≜ 𝑌𝑜 𝑙𝑈 min{ 𝐵𝑜 𝐹 [𝑙𝑈] , 𝐷𝑜 𝑙𝑈 σ𝑢=𝑙𝑈 𝑙+1 𝑈−1 𝑇𝑜 𝑢 } − 𝑁𝑓𝑜 (𝐹) σ𝑢=𝑙𝑈 𝑙+1 𝑈−1 𝑇𝑜[𝑢],
𝑁 > 0 is some parameter, 𝐵𝑜
(𝐹) 𝑙𝑈 + 𝐵𝑜 (𝑀) 𝑙𝑈 = 𝐵𝑜 𝑙𝑈 .
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). Strongly coupled Nonlinear ቄ
In JOS algorithm, the offloading decisions and wireless scheduling decisions are strongly coupled, which make it hard to implement Consider one time slot deadline setup, we build decoupled joint offloading and scheduling (DJOS) algorithm for the case with one time slot deadline. Based on the insight of one time slot DJOS, we developed DJOS for the general case. Decoupled Joint Offloading and Scheduling (DJOS) algorithm Wireless scheduling decisions Offloading decisions
Calculate WeightGap1 = 𝑋
1 (𝑀,𝐹) 𝑢 − 𝑋 1 (𝑀)[𝑢]
Calculate WeightGap2 = 𝑋
2 (𝑀,𝐹) 𝑢 − 𝑋 2 (𝑀)[𝑢]
Calculate WeightGapN = 𝑋
𝑂 (𝑀,𝐹) 𝑢 − 𝑋 𝑂 (𝑀)[𝑢]
User 𝟐 User 𝟑 User 𝑶
Step 2: Choose user 𝑜∗ 𝑢 ∈ 𝑏𝑠𝑛𝑏𝑦𝑜 WeightGapn for both wireless transmission and local computation, the rest users(𝑜 ≠ 𝑜∗[𝑢]) only perform local computations Step 3:
𝑋
𝑜 (𝑀,𝐹)[𝑢] and 𝑋 𝑜 (𝑀)[𝑢] are defined as follows:
𝑋
𝑜 (𝑀,𝐹) ≜
max
𝐵𝑜
𝑀 ,𝐵𝑜 𝐹
(𝑌𝑜 𝑢 min 𝐵𝑜
𝑀 , 𝜈𝑜 − 𝑁𝑓𝑜 𝑀 𝕞 𝐵𝑜
𝑀 >0 ) + (𝑌𝑜 𝑢 min 𝐵𝑜
𝐹 , 𝐷𝑜 𝑢
− 𝑁𝑓𝑜
𝐹 +
) 𝑋
𝑜 (𝑀) ≜ max 𝐵𝑜
(𝑀) ((𝑌𝑜 𝑢 min 𝐵𝑜
𝑀 , 𝜈𝑜 − 𝑁𝑓𝑜 𝑀 𝕞 𝐵𝑜
𝑀 >0 ))
Only local computation
Compute weight 𝑋
𝑜 (𝑀)[𝑢]
Both local computation and wireless transmission
Compute weight 𝑋
𝑜 (𝑀,𝐹)[𝑢]
Step 1:
𝑋
𝑜∗ (𝐹) 𝑢 ≥ 0
𝑋
𝑜∗ 𝑢 (𝐹) 𝑢 < 0
𝑋
𝑜∗ (𝑀) 𝑢 ≥ 0
𝐵𝑜∗
(𝐹)[𝑢] = min{𝐵𝑜∗ 𝑢 , 𝐷𝑜∗[𝑢]}
𝐵𝑜∗
(𝑀) 𝑢 = 𝐵𝑜∗ 𝑢 − 𝐵𝑜∗ 𝐹 [𝑢]
𝐵𝑜∗
(𝐹)[𝑢] = 0
𝐵𝑜∗
(𝑀) 𝑢 = 𝐵𝑜∗ 𝑢
𝑋
𝑜∗ (𝑀) 𝑢 < 0
𝐵𝑜∗
(𝐹)[𝑢] = 𝐵𝑜∗ 𝑢
𝐵𝑜∗
(𝑀) 𝑢 = 0
𝐵𝑜∗
(𝐹) 𝑢 = 𝐵𝑜∗ 𝑢
𝐵𝑜∗
(𝑀)[𝑢] = 0
For user 𝑜∗ that is allowed for both wireless transmission and local computations For users 𝑜 ≠ 𝑜∗ that are allowed for local computations only
𝑋
𝑜 (𝑀) 𝑢 ≥ 0
𝐵𝑜
(𝑀) 𝑢 = An[t]
𝑋
𝑜 (𝑀) 𝑢 < 0
𝐵𝑜
(𝑀) 𝑢 = 0
𝑋
𝑜∗ (𝐹)[𝑢], 𝑋 𝑜∗ (𝑀)[𝑢] and 𝑋 𝑜 (𝑀)[𝑢] are defined as follows:
𝑋
𝑜∗ (𝐹)[𝑢] ≜ 𝑌𝑜∗ 𝑢 min 𝐵𝑜∗ 𝑢 , 𝐷𝑜∗ 𝑢
− 𝑁𝑓𝑜∗
(𝐹)
𝑋
𝑜∗ (𝑀)[𝑢] ≜ 𝑌𝑜∗ 𝑢 min
𝐵𝑜∗
𝑀 [𝑢] − 𝐷𝑜∗[𝑢] +
, 𝜈𝑜∗ − 𝑁𝑓𝑜∗
𝑀
𝑋
𝑜 (𝑀)[𝑢] ≜ 𝑌𝑜 𝑢 min 𝐵𝑜 (𝑀) 𝑢 , 𝜈𝑜 − 𝑁𝑓𝑜 (𝑀)
Wireless scheduling decisions : Wireless scheduling decisions are obtained by solving the following optimization problem: 𝒛∗∈ argmax
𝒛
𝑜=1 𝑂
(𝑋
𝑜 (𝑧𝑜)(𝑀,𝐹) 𝑙𝑈 − 𝑋 𝑜 𝑀 [𝑙𝑈])
𝑜=1 𝑂
𝑧𝑜 = 𝑈 where 𝒛∗ = 𝑧𝑜
∗ 𝑜=1 𝑂
are the wireless scheduling decisions, 𝑧𝑜 denote the maximum number of wireless transmissions that are allowed for user 𝑜 in frame 𝑙. Offloading Decision: The offloading decisions for each user are similar with the case with one time slot 𝑃(𝑂𝑈) complexity
User 1: schedule 3 time slots User 2: schedule 2 time slots
𝑧1 = 3 𝑧2 = 2 𝑈 = 5 slots 𝑧1 + 𝑧2 = 𝑈
➢ 𝑂 = 5 users; ➢ Maximal allowable drop rate 𝜍 = 0.1; ➢ All users suffer from i.i.d ON-OFF channel fading; ➢ Local computation energy consumption 𝑓(𝑀) = 7 watt; ➢ Wireless transmission energy consumption 𝑓(𝐹) = 4 watt; ➢ Local processing rate 𝜈 = 1 The case with one time slot deadline The case with three time slot deadline Transmission rate 5 when the channel is ON Transmission rate 4 when the channel is ON 𝑌 = ቊ 5, 𝑞 = 𝜇/5 0,
𝑌 = ቊ 7, 𝑞 = 𝜇/7 0,
Where 𝑌 denotes number of arriving packets and 𝑞 denotes the probability that have arrivals.
The case with one time slot deadline ▪ Figure (a) implies that all users satisfy the maximum allowable drop rate ▪ Figure (b) shows that our proposed DJOS algorithm significantly saves the energy compared to LFOS ▪ Figure (c) studies the impact of parameter M
The case with three time slots deadline ▪ Figure (a) implies that all users satisfy the maximum allowable drop rate ▪ Figure (b) shows that our proposed DJOS algorithm significantly saves the energy compared to LFOS ▪ Figure (c) studies the impact of parameter M