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

From FNSSA_CRB’s point of view

\( {NTO}_t^A \)

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.

\( AD\_{MBCTO}_t^A \)

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.

\( {DATOP}_t^A \)

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.

\( En\_{RTO}_t^A \)

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.

\( {NC}_t^A \)

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.

\( En\_{RC}_t^A \)

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.

\( {NE}_t^A \)

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 R_m is submitted.

• R_{m :}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.

\( {RTtDeadline}_t^A \)

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

\( {NTO}_t^A \)

Number of Trading Opponents

See calculation formula in record # 1

\( AD\_{MBCTO}_t^A \)

Acceptance Degree of Mutual Behavior Class between an Agent A and its Trading Opponents

See calculation formula in record # 2

\( En\_{RTO}_t^A \)

Entrance Rate of Trading Opponents

See calculation formula in record # 4

\( {DATOP}_t^A \)

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.

\( {NC}_t^A \)

Number of Competitors

See calculation formula in record # 5

\( En\_{RC}_t^A \)

Entrance Rate of Competitors

See calculation formula in record # 6

\( {UL}_t^A \)

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.

\( {RTtDeadline}_t^A \)

Remaining Time to Negotiation Deadline

See calculation formula in record # 8