A queueing model with server breakdowns, repairs, vacations, and backup server

Timely Reliability Analysis of Virtual Machines Considering Migration and Recovery in an Edge Server

“…However, the failure of a server or a VM can reduce the processing capability of the edge node directly and increase latency [ 12 , 40 , 41 ]. To model the failure and repair of VMs, VMs can be treated as unreliable and repairable queue servers based on the multi-server queueing models with unreliable and repairable servers [ 20 , 21 , 22 , 23 , 26 ]. For instance, Ke et al [ 26 ] and Chakravarthy et al [ 23 ] analyzed multi-server queueing models considering unreliable servers and vacation policy.…”

“…To model the failure and repair of VMs, VMs can be treated as unreliable and repairable queue servers based on the multi-server queueing models with unreliable and repairable servers [ 20 , 21 , 22 , 23 , 26 ]. For instance, Ke et al [ 26 ] and Chakravarthy et al [ 23 ] analyzed multi-server queueing models considering unreliable servers and vacation policy. Although the unreliable and repairable servers in these queueing models are similar to VMs of the edge node, the present multi-server queueing models cannot be applied to model the edge computing servers directly.…”

“…All this considered, present studies on VM delay did not investigate the influence of VM migration on the total delay at the VMs, for the queueing models of VMs ignored the failure and migration of VMs [ 24 , 25 , 27 ], and the VM migration delay was measured separately from the total delay [ 12 , 13 , 14 , 42 , 44 , 45 , 46 , 47 , 53 ]. Meanwhile, due to the unique process of failure, migration, and recovery of VMs, present queueing models with unreliable servers [ 20 , 21 , 22 , 23 , 26 ] cannot be directly applied to analyze the VM delay. To analyze the timely reliability of the VMs and the network, we build a queueing model considering the whole process of failure, migration, and recovery of VMs and propose a method to obtain the PDF of the delay at the edge server.…”

“…To measure the timely reliability of edge computing more precisely, we need to build a queueing model considering failure, migration, and reboot of VM. Present mathematical models [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ] cannot take the migration of VM into account and neglect the migration downtime. Therefore, to analyze the edge computing system considering migration and recovery of VM, the essential migration-related states of VM need to be defined in a new evaluation model.…”

ANFIS and Cost Optimization for Markovian Queue with Operational Vacation

“…The concepts of both server breakdown and vacation have been presented by Kalyanaraman and Sundaramoorthy (2019) to study Markovian working vacation queueing model with state-dependent arrival rate and partial breakdown. Chakravarthy et al (2020) presented a queueing model for a service system with backup server during the absence of the main server. Rao et al (2017) analyze the two-phase Markovian queueing model where the first phase of service is for all waiting customers in batch mode and second phase of service is in individual mode.…”