# Table 1 Parameters that are used to model critical condition of the cloud trading market from both FNSSA_CRP’s and FNSSA_CRB’s points of view and their calculation formulas

# Parameter name Parameter definition Calculation formula
From FNSSA_CRB’s point of view 1 $${NTO}_t^A$$ Number of Trading Opponents $$\frac{\mathrm{no}.\mathrm{trading}\_{\mathrm{opponent}}_{\mathrm{t}}^{\mathbf{A}}}{\mathrm{no}.\mathrm{trading}\_{\mathrm{opponent}}_{\mathrm{t}}^{\mathbf{A}}+\mathrm{no}.{\mathrm{competitor}}_{\mathrm{t}}^{\mathbf{A}}}$$
Symbol Definition:
$$\boldsymbol{no}.\boldsymbol{trading}\_{\boldsymbol{opponent}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Number of trading opponents of negotiator A in tth round of negotiation.
$$\boldsymbol{no}.{\boldsymbol{competitor}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Number of competitors of negotiator A in tth round of negotiation.
2 $$AD\_{MBCTO}_t^A$$ Acceptance Degree of Mutual Behavior Class between an Agent A and its Trading Opponents $$\frac{\left[\left({\mathrm{percentage}}_t^{\mathrm{NLNH}}-{\mathrm{percentage}}_t^{\mathrm{LH}}\right)\times 100\right]+100\kern0.5em }{200}$$
Symbol Definition:
$${\boldsymbol{percentage}}_{\boldsymbol{t}}^{\boldsymbol{NRNH}}$$: Percentage of trading opponents with NLNH (not loyal and not hasty) mutual behavior class.
$${\boldsymbol{percentage}}_{\boldsymbol{t}}^{\boldsymbol{RH}}$$: Percentage of trading opponents with LH (loyal and hasty) mutual behavior class.
3 $${DATOP}_t^A$$ Distance from Average of Trading Opponents’ Proposals $$\frac{\sum \limits_{\mathrm{k}=1}^{\mathrm{no}.\mathrm{trading}\_{\mathrm{opponent}}_{\mathrm{t}-1}^{\mathbf{A}}}{\mathrm{P}}_{\mathrm{t}-1}^{{\mathrm{B}}_{\mathrm{k}}}-{\mathrm{P}}_{\mathrm{t}-2}^{\mathrm{A}}}{\sum \limits_{\mathrm{k}=1}^{\mathrm{no}.\mathrm{trading}\_{\mathrm{opponent}}_{\mathrm{t}-1}^{\mathbf{A}}}{\mathrm{P}}_{\mathrm{t}-1}^{{\mathrm{B}}_{\mathrm{k}}}\ }$$
Symbol Definition:
$$\sum \limits_{\boldsymbol{k}=\mathbf{1}}^{\boldsymbol{no.trading}\_{\boldsymbol{opponent}}_{\boldsymbol{t}-\mathbf{1}}^{\boldsymbol{A}}}{\boldsymbol{P}}_{\boldsymbol{t}-\mathbf{1}}^{{\boldsymbol{B}}_{\boldsymbol{k}}}$$: Average of counter-price offers of A’s trading opponents in negotiation round t-1.
$${\boldsymbol{P}}_{\boldsymbol{t}-\mathbf{2}}^{\boldsymbol{A}}$$: Counter-price offer of A in negotiation round t-2.
4 $$En\_{RTO}_t^A$$ Entrance Rate of Trading Opponents $$\frac{\mathrm{En}\_{\mathrm{TO}}_t^A-\operatorname{Min}\_\mathrm{En}\_{\mathrm{TO}}_t^A}{\operatorname{Max}\_\mathrm{En}\_{\mathrm{TO}}_t^A-\operatorname{Min}\_\mathrm{En}\_{\mathrm{TO}}_t^A\ }$$
Symbol Definition:
$$\boldsymbol{En}\_{\boldsymbol{TO}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Number of A’s trading opponents in the current market round t.
$$\boldsymbol{\operatorname{Min}}\_\boldsymbol{En}\_{\boldsymbol{TO}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Minimum number of trading opponents ever experienced by A up to negotiation round t.
$$\boldsymbol{\operatorname{Max}}\_\boldsymbol{En}\_{\boldsymbol{TO}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Maximum number of trading opponents ever experienced by A up to negotiation round t.
5 $${NC}_t^A$$ Number of Competitors $$\frac{\mathrm{no}.{\mathrm{competitor}}_{\mathrm{t}}^{\mathbf{A}}}{\mathrm{no}.\mathrm{trading}\_{\mathrm{opponent}}_{\mathrm{t}}^{\mathbf{A}}+\mathrm{no}.{\mathrm{competitor}}_{\mathrm{t}}^{\mathbf{A}}}$$
Symbol Definition:
$$\boldsymbol{no}.\boldsymbol{trading}\_{\boldsymbol{opponent}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Number of trading opponents of negotiator A in tth round of negotiation.
$$\boldsymbol{no}.{\boldsymbol{competitor}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Number of competitors of negotiator A in tth round of negotiation.
6 $$En\_{RC}_t^A$$ Entrance Rate of Competitors $$\frac{\mathrm{En}\_{\mathrm{C}}_t^A-\operatorname{Min}\_\mathrm{En}\_{\mathrm{C}}_t^A}{\operatorname{Max}\_\mathrm{En}\_{\mathrm{C}}_t^A-\operatorname{Min}\_\mathrm{En}\_{\mathrm{C}}_t^A\ }$$
Symbol Definition:
$$\boldsymbol{En}\_{\boldsymbol{C}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Number of A’s competitors in the current market round t.
$$\boldsymbol{\operatorname{Min}}\_\boldsymbol{En}\_{\boldsymbol{C}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Minimum number of competitors ever experienced by A up to negotiation round t.
$$\boldsymbol{\operatorname{Max}}\_\boldsymbol{En}\_{\boldsymbol{C}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Maximum number of competitors ever experienced by A up to negotiation round t.
7 $${NE}_t^A$$ Negotiator’s Eagerness for Hiring Resource Type Instances $$\frac{{\mathrm{A}\mathrm{TS}}_{\mathrm{t}}^{\mathrm{A}}+{\mathrm{RSRtMSR}}_{\mathrm{t}}^{\mathrm{A}}}{2\ }$$
Where:
$$A{TS}_t^A$$ = $$\frac{\sum \limits_{\boldsymbol{m}=\mathbf{1}}^{Tota l\_ no.{SRequests}_t^A}\left(\frac{\boldsymbol{t}-{t}_{entrance}^{R_m,A}}{t_{exit}^A-{t}_{entrance}^{R_m,A}}\right)}{Tota{l}_{no}.{SRequests}_t^A}$$
$${RSRtMSR}_t^A$$ = $$\frac{Total\_ no.{SRequests}_t^A}{MaxTotal\_{Requests}_t^A}$$
Symbol Definition:
$${\boldsymbol{t}}_{\boldsymbol{entrance}}^{{\boldsymbol{R}}_{\boldsymbol{m}},\boldsymbol{A}}$$: Negotiation market round in which Rm is submitted.
Rm :mth request of agent A.
$$\boldsymbol{Total}\_\boldsymbol{no}.{\boldsymbol{SRequests}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Total number of requests submitted by A up to current market round t.
$${\boldsymbol{t}}_{\boldsymbol{exit}}^{\boldsymbol{A}}$$: Exit time of A.
$$\boldsymbol{MaxTotal}\_{\boldsymbol{Requests}}_{\boldsymbol{t}}^{\boldsymbol{A}}:$$ Maximum number of requests submitted by the negotiator agent of type CRB in the negotiation market until current round t.
8 $${RTtDeadline}_t^A$$ Remaining Time to Negotiation Deadline $$\left\{\begin{array}{c}1-\left[\frac{\mathrm{t}-\left({\mathrm{t}}_{\mathrm{entrance}}^{\mathrm{A}}+{{\mathrm{Half}}_{\mathrm{t}}}_{\mathrm{deadline}}^{\mathrm{A}}\right)}{\left({\mathrm{t}}_{\mathrm{entrance}}^{\mathrm{A}}+{\mathrm{t}}_{\mathrm{deadline}}^{\mathrm{A}}\right)-\left({\mathrm{t}}_{\mathrm{entrance}}^{\mathrm{A}}+{{\mathrm{Half}}_{\mathrm{t}}}_{\mathrm{deadline}}^{\mathrm{A}}\right)}\right]\kern0.5em \mathrm{IF}\ \mathrm{condition}\ \mathrm{A}\kern0.75em \\ {}1\kern20em \mathrm{IF}\ \mathrm{condition}\ \mathrm{B}\ \end{array}\right.$$
Symbol Definition:
Condition A : $$t>{t}_{entrance}^A+ Half\_{t}_{deadline}^A$$.
Condition B: $$t\le {t}_{entrance}^A+ Half\_{t}_{deadline}^A$$.
$$\boldsymbol{Half}\_{\boldsymbol{t}}_{\boldsymbol{deadline}}^{\boldsymbol{A}}$$: Half of negotiator A’s deadline.
$${\boldsymbol{t}}_{\boldsymbol{entrance}}^{\boldsymbol{A}}$$: Time in which the negotiator agent A entrances to the negotiation market to purchase virtual machine types instances.
From FNSSA_CRP’s point of view 9 $${NTO}_t^A$$ Number of Trading Opponents See calculation formula in record # 1
10 $$AD\_{MBCTO}_t^A$$ Acceptance Degree of Mutual Behavior Class between an Agent A and its Trading Opponents See calculation formula in record # 2
11 $$En\_{RTO}_t^A$$ Entrance Rate of Trading Opponents See calculation formula in record # 4
12 $${DATOP}_t^A$$ Distance from Average of Trading Opponents’ Proposals $$\frac{{\mathrm{P}}_{\mathrm{t}-2}^{\mathrm{A}}-\sum \limits_{k=1}^{no. trading\_{opponent}_{t-1}^A}{\mathrm{P}}_{\mathrm{t}-1}^{{\mathrm{B}}_{\mathrm{k}}}}{{\mathrm{P}}_{\mathrm{t}-2}^{\mathrm{A}}}$$
Symbol Definition:
$$\sum \limits_{\boldsymbol{k}=\mathbf{1}}^{\boldsymbol{no.trading}\_{\boldsymbol{opponent}}_{\boldsymbol{t}-\mathbf{1}}^{\boldsymbol{A}}}{\mathbf{P}}_{\boldsymbol{t}-\mathbf{1}}^{{\boldsymbol{B}}_{\boldsymbol{k}}}\kern0.50em$$: Average of price-offers of A’s trading opponents in negotiation round t-1.
$${\mathbf{P}}_{\mathbf{t}-\mathbf{2}}^{\mathbf{A}}$$: Counter-price offer of A in negotiation round t-2.
13 $${NC}_t^A$$ Number of Competitors See calculation formula in record # 5
14 $$En\_{RC}_t^A$$ Entrance Rate of Competitors See calculation formula in record # 6
15 $${UL}_t^A$$ Utility Level $$\frac{{\mathrm{RC}}_{\mathrm{t}}^{\mathrm{A}}}{{\mathrm{TC}}_{\mathrm{t}}^{\mathrm{A}}}$$
Symbol Definition:
$${\boldsymbol{RC}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Rented resources of negotiator agent A up to negotiation round
$${\boldsymbol{TC}}_{\boldsymbol{t}}^{\boldsymbol{A}}$$: Total of supplied resources by negotiator agent A in the period of holding negotiation market.
16 $${RTtDeadline}_t^A$$ Remaining Time to Negotiation Deadline See calculation formula in record # 8