From: A cloud priority-based dynamic online double auction mechanism (PB-DODAM)
Symbols | Descriptions |
---|---|
S | Cloud service providers (sellers) |
B | Cloud service users (buyers) |
t | Time-slot |
t^{′} | Time (within each time-slot) |
α | Number of VMs (\(\alpha \in \mathbb {N}\)) |
θ_{i} | Type of agent i |
\(\hat \theta \) | Collection of all agents’ types |
\(\hat \theta ^{t}\) | Collection of all agents’ types in time-slot t |
\(\hat \theta ^{\leqslant t}\) | Collection of all agents’ types from the beginning |
till the end of time-slot t | |
v_{i} | The single unit valuation by agent i |
q_{i} | The total VMs’ quantity that agent i wants to trade |
a_{i} | The agent’s arrival time |
d_{i} | The agent’s departure time |
p | Agent’s presence period in a time-slot |
\(U_{i}^{\hat \theta ^{t}}\) | Seller’s i utility at time-slot t |
\(U_{j}^{\hat \theta ^{t}}\) | Buyer’s j utility at time-slot t |
P | Payment rule |
s_{i,j} | Seller’s obtained value from the auctioneer |
b_{i,j} | Buyer’s payment value to the auctioneer |
Q | Allocation rule |
M^{t} | Matchable pairs of asks and bids at time-slot t |
\(\sigma _{i}(\hat \theta ^{t})\) | Seller’s ask satisfiability in time-slot t |
\(c^{p}_{i}(\hat \theta ^{t})\) | Seller’s ask criticality in time-slot t and time t^{′} |
\(\sigma _{j}(\hat \theta ^{t})\) | Buyer’s bid satisfiability in time-slot t |
\(c^{p}_{j}(\hat \theta ^{t})\) | Buyer’s bid criticality in time-slot t and time t^{′} |
τ | Satisfiability threshold |
ϕ(t) | Market price |
\(e^{p}_{i}(t)\) | Agent i’s defer rate |
ε | Defer rate threshold |