Table 1 Key notation

\(eN{B}_{i}\)

edge server \({\mathrm{eNB}}_{\mathrm{i}}\)

\({C}_{i}\)

the computational capacity of edge server \({\mathrm{eNB}}_{\mathrm{i}}\)

\({B}_{i}\)

The bandwidth capacity of edge server \({\mathrm{eNB}}_{\mathrm{i}}\)

\({S}_{i}\)

The storage capacity of the edge server \({\mathrm{eNB}}_{\mathrm{i}}\)

\(V{M}_{i,j}\)

The jth VM in edge server \({\mathrm{eNB}}_{\mathrm{i}}\)

\({C}_{i,j}\)

The computational capacity of the VM \({\mathrm{VM}}_{\mathrm{i},\mathrm{j}}\)

\({B}_{i,j}\)

The bandwidth capacity of the VM \({\mathrm{VM}}_{\mathrm{i},\mathrm{j}}\)

\(S{E}_{k}\)

The service instance of service provider \({\mathrm{SP}}_{\mathrm{K}}\)

\({W}_{k}\)

the workload of the computation request processed by corresponding service instances \({\mathrm{SE}}_{\mathrm{k}}\)

\({D}_{k}\)

the size of the input data required by the computation request

\({g}_{i}\)

The coalition on the edge server \({\mathrm{eNB}}_{\mathrm{i}}\)

\({c}_{i,j}\)

the cost of the service provider occupying the VM \({\mathrm{VM}}_{\mathrm{i},\mathrm{j}}\) alone

\({d}_{k}^{CL}\)

The service latency of the computation request processed by the service instance \({\mathrm{SE}}_{\mathrm{k}}\) in the central cloud \(\mathrm{CL}\)

\({d}_{i,j,k}\)

The service latency of the computation request processed by the service instance \({\mathrm{SE}}_{\mathrm{k}}\) cached on VM \({\mathrm{VM}}_{\mathrm{i},\mathrm{j}}\) of edge server \({\mathrm{eNB}}_{\mathrm{i}}\)

\({d}_{i,j,k}^{exe}\)

The service execution latency of the computation requests processed by service instance \({\mathrm{SE}}_{\mathrm{k}}\) cached on VM \({\mathrm{VM}}_{\mathrm{i},\mathrm{j}}\) of edge server \({\mathrm{eNB}}_{\mathrm{i}}\)

\({d}_{i,k}^{tran}\)

The transfer time of input data required by service instance \({\mathrm{SE}}_{\mathrm{k}}\)

\({v}_{k}\)

Delay preference weight