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# Table 1 Notations and mapping of multitenancy problem to QN model and MMKP

From: Optimal deployment of components of cloud-hosted application for guaranteeing multitenancy isolation

Notation | Multitenancy isolation problem | MMKP | QN model |
---|---|---|---|

N | Total number of groups of components | Total number of groups of objects | Total number of classes |

l | Total number of items in a group | Total number of objects in a group | - |

m (K is used for QN) | Total number of resources | Total number of resources | Total number of service centers |

α (k is used for QN)
| Index for resource supporting a component | Index for resource supporting a component | Index for service centers |

i (c is used for QN) | Index value for the Group | Index value for the Group | Index value for the Class |

j | Index value for the component | Index value for the object | - |

a
_{
ij}
| A component which is associated with isolation value, number of requests, cpu, ram, disk and bandwidth size | Objects in a group | - |

c |
Group of component (c_{1},...,c_{N})
| Group of objects | Class |

\(r_{ij}^{\alpha }\) | Resource consumption of each component | Resources required by the object in the knapsack | Service centres in the system (cpu, ram, disk, bandwidth) |

R | Limit of each resource supporting each component (R(=1,m)) | Resources available in the knapsack (knapsack capacity) | System/Component capacity |

I
_{
ij}
| Isolation value for a component.Used to compute G. | - | - |

Q
_{
ij}
| The number of requests allowed to access a component. Used to compute G | - | The queue length of class c at centre k, |

D
_{
c,
k}
| The service demands at the cpu,ram,disk, and bandwidth | - | Service demand of class c at k service centres (cpu, ram, disk, bandwidth) |

λ
_{
ij}
| Workload on the component (arrival rate of request to the component/system) | - | Workload on the component (arrival rate of request to the component/system) |

g
_{
ij}
| Optimal value for one component in a group | Profit of one object in MMKP | - |

\(\mathcal {G}\) | Optimal function of the solution | Profit of the solution in MMKP | - |