System Model and Problem Formulation

Resource Management

3.2 System Model and Problem Formulation

In this section, we discuss the proposed optimization model for cost-aware placement of data-intensive applications in federated cloud DCs. Table 3.1 summarizes the notation used. First, we state the system model and the assumptions made, before presenting the optimization model.

3.2.1 Assumptions

• We consider the initial placement of virtual components assuming that the entire resource requirement of an application is less than the total capacity of the system.

• The requirements of virtual components and the capacity of the DCs are heterogeneous.

• The bandwidth cost within a DC is negligible, and there is no restriction on the bandwidth usage. The inter-DC bandwidth cost depends on the location [53, 125].

3.2. System Model and Problem Formulation

• The cost of a resource used is based on its energy consumption. We use the electricity price at the location of a DC as the pricing factor for CPs [76].

• FCMs exchange information that includes the DC identifier, the available resources in the DC, the current electricity price, and the PUE (see Eq. 3.1).

Table 3.1: Notation used in the system model Symbol Description

P Set of cloud providers in the federation

F Set of federated cloud managers in the federation D Set of data centers in the federation

D_p Set of the data centers of thep^th cloud provider D_pk k^th data center of cloud providerp

D_pk^cpu CPU capacity of data center D_pk D_pk^mem Memory capacity of data center D_pk D_pk^str Storage capacity of data center D_pk

E_pk Electricity price at data centerD_pk (in $/KWh) P U E_pk Power usage effectiveness at data center D_pk s_pk The number of servers at data center D_pk P_pk Power consumption of data center D_pk (KWh) DPpk,ql Data transfer price between D_pk and D_ql ($/GB) BW_pk,ql The bandwidth of the link between D_pk and D_ql (Gbps) C Set of virtual components

V Set of virtual machines B Set of data blocks

V M_i^cpu CPU demand of i^th virtual machine V M_i^mem Memory demand of i^th virtual machine DB_j^str Storage demand of j^th data block

x^pk_i Virtual component iis assigned to data centerD_pk Aji Traffic demand between two components j and i(GB/h) SPv Power consumed by server v (in KWh)

BP_v Base power consumed by serverv when idle

F P_v^r Power consumed by resource r in server vat full utilization U_v^r Utilization of resource r in serverv

C_v^r Capacity of resource r in serverv

z_v binary variable that indicates if server v is used or not t The running time of the application (in hours)

3. Placement of Data-intensive Applications on Federated Cloud

3.2.2 System Model

LetP denote the set of collaborating CPs in a federated cloud. Each cloud providerp in the federation has a set of data centersD_p and an FCM Fp. LetF={F_p, p∈P} be the set of all FCMs andD={D_p, p∈P} be the set of all DCs in the federated cloud. Each data center in the federation D_pk ∈D is characterized by its CPU capacityD^cpu_pk , memory capacity D_pk^mem, storage capacityD_pk^str, power usage effectiveness P U E_pk, and its operating cost in terms of electricity price Epk. We assume that the supply of these resources is controlled and can be changed by the CP. Accordingly, an FCM, sayF_p has a freedom to announce the resource capacity available for sharing at each of its data centers, sayD_pk. We define the network bandwidth between data centers by a matrixBW_|D|×|D|, whereBW_pk,ql represents the bandwidth of the link between a data centerD_pk and another oneD_ql.

User Request: A CP receives a request for multiple virtual components. Let Cbe the set of all virtual components needed by the application, which is a union of two subsets;V, the set of compute virtual machines andB, the set of data blocks. Each virtual machine V Mi∈V demands a number of CPU cores,V M_i^cpu and memory, V M_i^mem (perGB), while each data blockDB_j ∈Bcomes only with a storage demand, DB_j^str (per GB).

The application request is represented as a weighted directed graph G(C, W), whereCis the set of virtual components, and W is the set of weighted edges that represent the traffic demand between the virtual components. Figure. 3.2 depicts a typical application request with squares indicating the data blocks and circles indicating the compute VMs. A weighted edge is directed from a source V M (or DB) to a destinationV M, and its thickness reflects the variation in the traffic demand. Data-intensive applications are usually characterized by high traffic between DBs and V M s, low traffic amongV M s and no traffic between DBs [53]. We define C as a multi-dimensional vector, where each dimension represents a type of resource; CPU, memory and storage. We represent the traffic demand by an adjacency matrixA_|C|×|V|, whereA_ji is the data volume betweenDB_j (or V M_j) and V M_i. We define also a binary variablex^pk_i to indicate whether a virtual componentV Ci ∈Cis placed in the data centerD_pk (x^pk_i = 1) or not (x^pk_i = 0).

Power consumption: Though power consumption is usually modeled as a function of only the CPU utilization, it was noted that the storage may consume up to 40% of the total

3.2. System Model and Problem Formulation

Figure 3.2: Graph representation of a data-intensive application request

energy of a data center for data-intensive applications [50]. Accordingly, in this chapter, we consider CPU and storage to consume a significant portion of power [50]. The total power consumed by a serverv is expressed as

SP_v =BP_v+X

r

F P_v^r∗U_v^r

C_v^r (3.2)

whereBP_v is the base power consumption of a serverv, andF P_v^r is the power consumed by a resourcer of a serverv at full utilization. r∈ {CP U, Storage} is the concerned resource, U_v^r andC_v^r are the utilization and maximum capacity of the resourcer in a server v. The power consumption of an entire data centerD_pk also includes the power consumed by the other data center facilities, such as cooling system, that might account for 50% of the total energy based on the location [50]. We define the total power consumed (KWh) at a data centerD_pk housing s_pk servers as

Ppk =

spk

X

v=1

SPv∗zv∗P U Epk (3.3) wherez_v is a binary variable set to unity when the server vis being used and P U E_pk is the power usage effectiveness of a data centerD_pk.

3. Placement of Data-intensive Applications on Federated Cloud

3.2.3 Optimization Model

Next, we define the cost components of TCO considered in the formulation of the optimization problem in this chapter.

Energy cost: The cost incurred by power at a data center D_pk can be obtained by multiplying power usage P_pk ofD_pk (Eq.3.3) with the electricity price E_pk ($/KWh). The energy cost incurred by the federation per hour ($/h) is the summation of the energy consumption cost of all data centers of the federation, and it is defined as

EC= X

D_pk∈D

P_pkE_pk (3.4)

Communication cost: Comparing to inter-DC bandwidth cost, the communication cost is negligible for virtual components within a DC [53]. We define the communication cost due to data-intensive applications deployed within the federationCC as

CC= X

D_pk∈D

X

D_ql∈D D_pk6=D_ql

X

i∈C

X

j∈V

x^pk_i x^ql_jA_ijDP_pk,ql (3.5)

whereAij is the data transfer requirement between V Ci and V Mj (in GB/h) andDPpk,ql

is the data transfer cost betweenD_pk and D_ql ($/GB).

Using all the cost factors considered above, we formulate the optimization model as

Minimize (EC+CC)t (3.6)

subject to

X

D_pk∈D

x^pk_i = 1, ∀i∈C (3.7)

X

j∈V

x^pk_j V M_j^cpu ≤ D^cpu_pk , ∀D_pk ∈D (3.8)

X

j∈V

x^pk_j V M_j^mem ≤ D^mem_pk , ∀D_pk ∈D (3.9)