A scalable and automatic mechanism for resource allocation in self-organizing cloud

Abstract

Taking advantage of the huge potential of consumers’ untapped computing power, self-organizing cloud is a novel computing paradigm where the consumers are able to contribute/sell their computing resources. Meanwhile, host machines held by the consumers are connected by a peer-to-peer (P2P) overlay network on the Internet. In this new architecture, due to large and varying multitudes of resources and prices, it is inefficient and tedious for consumers to select the proper resource manually. Thus, there is a high demand for a scalable and automatic mechanism to accomplish resource allocation. In view of this challenge, this paper proposes two novel economic strategies based on mechanism design. Concretely, we apply the Modified Vickrey Auction (MVA) mechanism to the case where the resource is sufficient; and the Continuous Double Auction (CDA) mechanism is employed when the resource is insufficient. We also prove that aforementioned mechanisms have dominant strategy incentive compatibility. Finally, extensive experiment results are conducted to verify the performance of the proposed strategies in terms of procurement cost and execution efficiency.

Appendix A: Proof of Theorem 1

We introduce [15] and prove as follows.

Proof

First of all, we consider bidder 1. His value is v _1j and bid is b _1j . The other bidders have bids b _2j , ... , b _{n j} and valuations v _2j , ... , v _{n j} . Due to the reverse auction, the utility value of bidder 1 is b _1j − v _1j . We consider the following cases.

Case 1: v _1j ≤ m i n(b _2j , ... , b _{n j} ). There are two sub-cases here: b _1j ≤ m i n(b _2j , ... b _{n j} ) and b _1j > m i n(b _2j , ... b _{n j} )).

Case 2: v _1j >m i n(b _2j , ... , b _{n j} ). There are two sub-cases here: b _1j ≤ m i n(b _2j , ... b _{n j} ) and b _1j > m i n(b _2j , ... b _{n j} )).

We analyze these cases separately below.

Case 1: v _1j ≤ m i n(b _2j , ... , b _{n j} ).

• Let b _1j ≤ m i n(b _2j , ... b _{n j} ). This implies that bidder 1 is the winner, which refers that u _1j = m i n(b _2j , ... b _{n j} )−v _1j ≥ 0.

• Let b _1j >m i n(b _2j , ... b _{n j} ). This means that bidder 1 is not the winner, which in turn means that u _1j = 0.

• Let b _1j = v _1j , then since v _1j ≤ m i n(b _2j , ... , b _{n j} ), we have u _1j = m i n(b _2j , ... b _{n j} )−v _1j .

Thus, if b _1j = v _1j , the utility u _1j is greater than or equal to the maximum utility obtainable. Thus, whatever the values of b _2j , ... b _{n j} , it is a best response for player 1 to bid v _1j . Thus, b _1j = v _1j is a weakly dominant strategy for bidder 1.

Case 2: v _1j >m i n(b _2j , ... , b _{n j} ).

• Let b _1j ≤ m i n(b _2j , ... b _{n j} ). This implies that bidder 1 is the winner, and the payoff is given by u _1j = m i n(b _2j , ... b _{n j} )−v _1j < 0.

• Let b _1j >m i n(b _2j , ... b _{n j} ). This means that bidder 1 is not the winner. Therefore u _1j = 0.

• Let b _1j = v _1j , then bidder 1 is not the winner and thus u _1j = 0.

From the above analysis, it is clear that b _1j = v _1j is a best response strategy for player 1 in Case 2 also. Combining our analysis of Case 1 and Case 2, we have that

$$u_{1j}(v_{1j},b_{2j},...,b_{nj})\geq u_{1j}(\widehat{b_{1j}},b_{2j},...,b_{nj}) $$

where $\widehat {b_{1j}} \in {\Theta }_{1j}, \forall b_{2j}\in {\Theta }_{2j},...,b_{nj}\in {\Theta }_{nj}$.

Also, we can show that, for any $b_{1j}^{\prime } \neq v_{1j}$, we can always find that for ∀b _2j ∈ Θ_2j , ... , b _{n j} ∈ Θ _{n j} , such that

$$u_{1j}(v_{1j},b_{2j},...,b_{nj})\geq u_{1j}(b_{1j}^{\prime},b_{2j},...,b_{nj}) $$

Thus b _1j = v _1j is a weakly dominant strategy for bidder 1. Using almost similar arguments, we can show that b _{i j} = v _{i j} is a weakly dominant strategy for bidder i where i = 2, ... , n. Therefor v _1j , ... , v _{n j} is a weakly dominant strategy equilibrium. □