## 4 Proposed Algorithm (NCRA-DP-ACO)
### Pheromone Management
#### 4.2.7 Algorithm
#### 5.2.4 Number of Live Migrations

In our experimental evaluation of live VM migrations, we focused on comparing the NCRA-DP-ACO algorithm against UACS because both approaches implement dynamic VM migration strategies during operation. In contrast, traditional heuristic algorithms such as BFD, FFD, and CRADP perform static initial VM placements without continuous migration. These static heuristics do not actively monitor server utilization after placement or initiate migrations to optimize energy consumption or SLA compliance. Therefore, including them in the live migration comparison would not add insight, as their designs inherently lack dynamic re-optimization features. ACO implemented the balanced migration strategy, which involved dynamic placement optimization with a minimum SLA impact, whereas UACS exhibited a higher frequency of migration without the use of any SLA or cost benefits, as shown in Figure 8.

Figure 7: Total cost comparison for varying workload sizes across proposed ACO and baseline algorithms. #### 5.2.5 Average Host Uptime

Host uptime sums the total active time of PMs during placements. An effective VMP strategy consolidates workloads onto fewer hosts, reducing the active time, energy consumption, and cost. As illustrated by Figure 9, the proposed ACO presents substantially lower average host uptimes. ACO consolidates the VMs into fewer active servers while allowing the remaining machines to go low-power or even idle, thus saving energy. #### 5.2.6 SLA Violations

The following areas were considered regarding SLA violations:

1. PDM (Performance Degradation due to Migrations)

PDM measures the performance degradation suffered by VMs due to their live migrations. Live migrations are essential operations that move VMs from one host to another without shutting them down. Performance degradation usually refers to a reduction in the quality of service (QoS) or performance of a VM during or after migration. This may refer to increased latency, reduced throughput, or higher response times. Figure 8: Number of live VM migrations of proposed ACO versus UACS across varying workload sizes. Figure 9: Average host uptime (s) for proposed ACO and baseline algorithms for increasing workload sizes. This metric helps operators understand trade-offs between migrating VMs for load balancing and preserving performance. \[PDM=\frac{1}{|VM|}\sum_{j\in VM}^{VM}\frac{VM_{j}^{pdm}}{VM_{j}^{MIPS}}\]

\(|\)\(VM|\) is the number of VMs; \(VM_{j}^{pdm}\) is the estimate of the performance degradation of \(VM_{j}\) caused by migrations (taken as 10% as in [39]); and \(VM_{j}^{CPU}\) is the total \(CPU\) capacity requested by the \(VM_{j}\) during its lifetime. In other words, PDM is a percentage that measures how good the initial VM placement decision was; a lower PDM percentage means better placement and consequently fewer migrations needed. Figure 10 shows the stability of the placement quality using the PDM metric. 2. SLATAH (SLA Time per Active Host)

SLATAH captures the average time that each active host spends in SLA violation. An SLA violation occurs when a host fails to meet performance or availability standards for its VMs. The conditions leading to SLA violations can include a lack of resource contention, overloading, or the intervention of any other issues affecting the performance of the VM. Figure 5.0

SLAV is a composite index that represents the total SLA violations calculated from performance degradation (PDM) and the time during which the SLA is violated (SLATAH) [39]. Figure 5.1

It provides insight into the effect of migrations and resource contention on overall SLA compliance. Figure 11 illustrates the SLA violations. Figure 5.2 Placement degradation metric (_PDM_) comparison for proposed ACO and UACS across varying workload sizes.