Utilization-Driven Performance Enhancement in Storage Area Networks

Abstract

Efficient resource utilization and low response times are critical challenges in storage area network (SAN) systems, especially as data-intensive applications like those driven by the Internet of Things and Artificial Intelligence place increasing demands on reliable, high-performance data storage solutions. Addressing these challenges, this paper contributes by proposing a proactive, utilization-driven traffic redistribution strategy to achieve balanced load distribution across switches, thereby improving the overall SAN performance and alleviating the risk of overload-incurred cascading failures. The proposed approach incorporates a Jackson Queueing Network-based method to evaluate both utilization and response time of individual switches, as well as the overall system response time. Based on a comprehensive case study of a mesh SAN system, two key parameters—the transition probability adjustment step size and the node selection window size—are analyzed for their impact on the effectiveness of the proposed strategy, revealing several valuable insights into fine-tuning traffic redistribution parameters.

1. Introduction

Modern data-intensive applications such as those driven by the Internet of Things and Artificial Intelligence place growing demands on high-performance data storage solutions [1]. These applications abound in mission-critical domains such as autonomous driving, real-time financial trading, industrial automation, and healthcare monitoring, all of which require scalable and reliable storage backends capable of handling large volumes of data with low latency. To meet these demands, enterprises such as NetApp, Tintri, and IBM have adopted storage area networks (SANs) as a foundational component of their data center infrastructure [2]. SANs enable high-speed, any-to-any connectivity between servers and storage devices within a dedicated network, offering benefits such as high throughput and concurrent data access [3,4,5]. These characteristics make SANs particularly suitable for enterprise environments where performance and reliability are essential.

A significant threat to the reliable operation of SANs is node overloading, potentially triggering a chain reaction that crashes the entire system, referred to as cascading failures [6,7,8,9]. Specifically, when a SAN device is overloaded and operating at a high utilization rate while others remain underutilized, this imbalance in load and utilization across devices increases the risk of failure in the bottleneck node. If a node fails, its entire load is redistributed to other nodes, potentially causing overloads on those nodes in a domino effect, which ultimately leads to a system-wide outage. To effectively prevent cascading failures, it is pivotal to proactively redistribute the load of highly utilized nodes before they reach certain critical levels. By doing this early, the risk of overloading any single node could be mitigated, helping to maintain load balancing across nodes and prevent cascading failures that lead to widespread system malfunction.

Therefore, in this paper we make unique contributions by proposing a proactive, utilization-driven load/traffic redistribution strategy to enhance the performance of SAN systems. Through monitoring the utilization levels of nodes and redistributing traffic before a pre-specified critical threshold is reached, our strategy aims to prevent node overloading and ensure a more balanced load distribution across the SAN, thereby alleviating the risk of cascading failures.

Cascading failures have been studied using simulations, self-organized critical models, and complex network models mainly in the power system domain [10,11]. Their effects on system reliability have been examined via topological approaches, combinatorial approaches, state-based approaches, and simulations [9]. Various mitigation strategies were proposed [12], including but not limited to those based on source detection [13], vulnerable node identification [14], topological dependence [15], interdependencies [16], system operating characteristics [17], resource allocation [18], redundant capacity [19], resilience assessment [20], and dynamic healing mechanism [21]. Recently, there are several attempts to mitigate cascading failures for SAN systems from the perspective of reliability, including load redistribution triggered by SAN reliability [22] and by individual switch workload [23]. To the best of our knowledge, no systematic study has been conducted to address the mitigation of overload-incurred cascading failures from a performance enhancement perspective like this work.

To verify the effectiveness of the proposed strategy, we make further contributions by conducting performance modeling and analysis of SAN systems. A Jackson Queueing Network (JQN)-based method is adapted for assessing the utilization and response time of individual switches, and the overall system response time. A detailed case study of a mesh SAN system is conducted. The impact of two key parameters in the proposed strategy (the transition probability adjustment step size and the node selection window size) is also examined.

The rest of the paper is structured as follows: Section 2 introduces the JQN model used for performance analysis of SAN. Section 3 describes the proposed utilization-driven performance enhancement strategy. Section 4 presents an example of a mesh SAN. Using the example SAN system, Section 5 examines the effects of key parameters on the effectiveness of the proposed strategy. Section 6 gives the conclusion and highlights several future research directions.

2. Jackson Queuing Network-Based Performance Evaluation

Jackson queueing networks (JQNs) have been applied to the performance analysis of diverse systems. For example, the vehicle waiting time of a road network was modeled using a JQN model for implementing an autonomous and intelligent traffic management system [24]. An open JQN was applied to optimize the average latency of all service function chains in an edge-core network efficiently [25]. An iterative algorithm was investigated to analyze the age of information of a JQN with finite buffer size in various settings [26]. A general quantum JQN was proposed to analyze the optimal pumping rates and routing probabilities of repeater-assisted and repeater-less quantum networks [27]. However, to the best of our knowledge, JQN has not been applied to model the performance of a SAN system. In this work, we first apply the JQN to assess the utilization and response time of SAN systems subject to the utilization-driven dynamic load redistributions for performance enhancement. Below we describe the fundamentals of JQN; readers may refer to [28,29] for more details.

A JQN is a queueing network with K nodes satisfying the following three conditions [29]:

1.

Each node k (k = 1, 2, …, K) consists of c_k identical servers with service time following the exponential distribution characterized by a constant service rate μ_k.

2.

Customers from outside the system arrive at node k following a Poisson process with arrival rate λ_k.

3.

Once served at node k, a customer goes to node j (j = 1, 2, …, K) with probability P_kj; or leaves the network with probability $1-{\sum }_{j=1}^K{P}_{kj}$. Thus, the average arrival rate to each node k, denoted by Λ_k, can be evaluated as

$${\Lambda }_k={\lambda }_k+{\sum }_{j=1}^K{\Lambda }_j{P}_{jk}$$

(1)

Equation (1) is known as a traffic equation, implying that the average arrival rate Λ_k of each node k includes both external customer arrivals λ_k and arrivals from other nodes within the network. Λ_k can be obtained by solving the traffic equations for all the nodes in the JQN.

The utilization of a node represents an average fraction of the time that each node is busy assuming that the traffic is evenly distributed to each node. For a node k with c_k identical servers, service rate μ_k and average arrival rate Λ_k, its utilization (denoted by ${\rho }_k$) is formulated as [28].

$${\rho }_k={\displaystyle \frac{{\Lambda }_k}{{c_k\mu }_k}}$$

(2)

Let $\pi$(n₁, n₂, …, n_K) denote the joint steady state probability that there are $n_k$ customers in node k for k = 1, 2, …, K. Let $p_k\left(n_k\right)$ be the steady state probability that there are $n_k$ customers in node k, which can be derived by modeling each node as an independent M/M/c_k queueing system with average arrival rate Λ_k. With ${\pi }_k\left(n_k\right)$ derived, we can obtain $\pi \left(n_1,n_2,\dots ,n_K\right)$ as ${\pi }_1\left(n_1\right){\pi }_2\left(n_2\right)\dots {\pi }_K\left(n_K\right)$ based on Jackson’s Theorem [28].

In the context of the SAN, each node can be modeled as an M/M/1 queue system (i.e., c_k = 1) with ${\pi }_k\left(n_k\right)={\left({\rho }_k\right)}^{n_k}\left(1-{\rho }_k\right)$ [28]. The average response time at node k with average service time being ${\displaystyle \frac{1}{{\mu }_k}}$ is

$$W_k={\displaystyle \frac{\frac{1}{{\mu }_k}}{1-{\rho }_k}}$$

(3)

According to Little’s Law, the average number of jobs in node k is

$$L_k={\Lambda }_k{W}_k$$

(4)

Further, based on Little’s Law, the overall mean response time of the entire JQN is the total average number of jobs in all nodes of the network divided by the total external arrival rates, formulated as

$$W={\displaystyle \frac{1}{\sum _{k=1}^K{\mathsf{\lambda }}_k}}{\sum }_{i=1}^K{L}_i$$

(5)

3. Utilization-Driven Performance Enhancement Strategy

We explore a utilization-driven traffic/load redistribution strategy to enhance the performance of SAN systems. Specifically, when a switch’s utilization reaches a pre-defined initial threshold ρ* (i.e., the switch gets too busy), we strategically reallocate the traffic by adjusting the transition probabilities for a set of vulnerable nodes selected based on rules detailed in the following subsections. As the utilization of 0.8 is commonly regarded as the limit of acceptable performance, in this study, we adopt this value as the threshold, i.e., ρ* = 0.8. The same threshold ρ* is used for triggering traffic redistribution during the entire mission.

3.1. Node Selection Rule

When the utilization of any node (e.g., switch in SAN) reaches ρ*, this node together with other nodes within the selection window w are chosen for traffic redistribution by adjusting their transition probabilities. Specifically, all nodes with utilization falling within the range [ρ* − w, ρ*] are selected. For example, if ρ* = 0.8 and the selection window size is w = 0.1, then all nodes with utilization between 0.7 and 0.8 are chosen for transition probability adjustment according to the ascending order of their utilization values, as detailed in Section 3.2. Note that only switches in the SAN participate in the transition probability adjustment or can be selected.

3.2. Transition Probability Adjustment Strategy

Assume node j’s utilization reaches the threshold ρ*. Equation (6) is applied to adjust the transition probabilities of nodes falling in the adjustment window, as discussed in Section 3.1. Let A_j represent the set of nodes selected for adjustment triggered by node j’s utilization. Specifically, for node $k\in$ ${\mathit{A}}_j$, let ${\mathit{N}}_k$ denote the set of neighboring nodes for node k. For any node i $\in {\mathit{N}}_k$, their transition probabilities to node k, i.e., $P_{ik}$ are adjusted according to (6), where s represents the step value of the adjustment.

$${P_{ik}=P}_{ik}-s$$

(6)

To make sure ${\sum }_{\forall r\in {\mathit{N}}_{\mathit{i}}}{P}_{ir}$ = 1, we need to adjust the transition probabilities from node i to all other neighboring nodes other than node k. Particularly, for any $r\in {\mathit{N}}_i$ and $r\ne k$, $P_{ir}$ is adjusted according to (7).

$${P_{ir}=P}_{ir}+{\displaystyle \frac{s}{\left|{\mathit{N}}_i\right|-1}}$$

(7)

4. Illustrative Example

Figure 1 illustrates an example of a mesh SAN used for evaluating the proposed performance enhancement strategy. There are two servers (Sr₁ and Sr₂) providing data request services (initiating read/write operations), and two storage arrays (Sa₁ and Sa₂) fulfilling these data requests over a dedicated high-speed network composed of switches. The five switches (Sw₁, Sw₂, Sw₃, Sw₄, Sw₅) in the example SAN facilitate any-to-any communications between the servers and the storage arrays. Each switch has an exponential service time distribution with constant rate μ_k, k ∈ {Sw₁, Sw₂, Sw₃, Sw₄, Sw₅} with values given in

Table 1. Baseline average service rate for the five switches.

Switch	Average Service Rate μ (Gb/s)
Sw1	16
Sw2	20
Sw3	25
Sw4	18
Sw5	30

. Those rates are given based on technical specifications of products in the industry [30,31,32].

4.1. JQN Modeling

To evaluate the performance of the example SAN using the JQN, each SAN component is modeled using a node as shown in Figure 2, where Sr₁ and Sr₂ are modeled by nodes 1 and 2, respectively, Sa₁ and Sa₂ are modeled by nodes 8 and 9, respectively, the five switches are modeled by node 3 through node 7. The links that connect the SAN components (e.g., fiber optics) correspond to the edges that connect the nodes in the JQN. Moreover, for evaluating traffic equations, two dummy nodes are added. The dummy node 0 is connected to node 1 and node 2, while node 8 and node 9 are connected to the dummy node 10. In this work, only node 0 has a non-zero external arrival rate λ₀, which is simplified as λ in the subsequent discussions.

The traffic equations for the eleven nodes of the JQN in Figure 2 are provided in (8).

$$\begin{array}{}{\Lambda }_0=\lambda \\ {\Lambda }_1={\Lambda }_0{P}_{\mathrm{0,1}}+{\Lambda }_3{P}_{\mathrm{3,1}}+{\Lambda }_4{P}_{\mathrm{4,1}}\\ {\Lambda }_2={\Lambda }_0{P}_{\mathrm{0,2}}+{\Lambda }_4{P}_{\mathrm{4,2}}+{\Lambda }_7{P}_{\mathrm{7,2}}\\ {\Lambda }_3={\Lambda }_1{P}_{\mathrm{1,3}}+{\Lambda }_4{P}_{\mathrm{4,3}}+{\Lambda }_5{P}_{\mathrm{5,3}}+{\Lambda }_6{P}_{\mathrm{6,3}}+{\Lambda }_7{P}_{\mathrm{7,3}}\\ {\Lambda }_4={\Lambda }_1{P}_{\mathrm{1,4}}+{\Lambda }_2{P}_{\mathrm{2,4}}+{\Lambda }_3{P}_{\mathrm{3,4}}+{\Lambda }_5{P}_{\mathrm{5,4}}+{\Lambda }_6{P}_{\mathrm{6,4}}+{\Lambda }_7{P}_{\mathrm{7,4}}\\ {\Lambda }_5={\Lambda }_3{P}_{\mathrm{3,5}}+{\Lambda }_4{P}_{\mathrm{4,5}}+{\Lambda }_6{P}_{\mathrm{6,5}}+{\Lambda }_8{P}_{\mathrm{8,5}}\\ {\Lambda }_6={\Lambda }_3{P}_{\mathrm{3,6}}+{\Lambda }_4{P}_{\mathrm{4,6}}+{\Lambda }_5{P}_{\mathrm{5,6}}+{\Lambda }_7{P}_{\mathrm{7,6}}+{\Lambda }_8{P}_{\mathrm{8,6}}+{\Lambda }_9{P}_{\mathrm{9,6}}\\ {\Lambda }_7={\Lambda }_2{P}_{\mathrm{2,7}}+{\Lambda }_3{P}_{\mathrm{3,7}}+{\Lambda }_4{P}_{\mathrm{4,7}}+{\Lambda }_6{P}_{\mathrm{6,7}}+{\Lambda }_9{P}_{\mathrm{9,7}}\\ {\Lambda }_8={\Lambda }_5{P}_{\mathrm{5,8}}+{\Lambda }_6{P}_{\mathrm{6,8}}\\ {\Lambda }_9={\Lambda }_6{P}_{\mathrm{6,9}}+{\Lambda }_7{P}_{\mathrm{7,9}}\\ {\Lambda }_{10}={\Lambda }_8{P}_{\mathrm{8,10}}+{\Lambda }_9{P}_{\mathrm{9,10}}\end{array}$$

(8)

Solving those traffic equations, the average arrival rate to each node k, i.e., Λ_k for k = 0, 1, …, 10 can be obtained. In this work, we use MATLAB R2023b to solve the traffic equations.

4.2. Initialization of Transition Probabilities

Let M represent the total number of SAN servers. At the beginning, the transition probability from node 0 to each SAN server is calculated as ${\displaystyle \frac{1}{M}}$. Later, each time the traffic redistribution condition is triggered, the transition probability from node 0 to server n, denoted as $P_{0,n}$ is updated using the following rule: Let l_n denote the total number of paths through which server n is connected to the switch being adjusted, i.e., a node $k\in$ ${\mathit{A}}_j$ as discussed in Section 3.2. The transition probability $P_{0,n}$ is adjusted using (9).

$$P_{0,n}={\displaystyle \frac{l_n}{\sum _{i=1}^M{l}_i}}$$

(9)

In our case, since M = 2, the initial transition probabilities are $P_{\mathrm{0,1}}=P_{\mathrm{0,2}}=0.5$. When the first traffic redistribution takes place, according to the rules defined in Section 3.1, the switch being adjusted first is node 4 (i.e., Sw₂). The total number of paths from servers 1 and 2 to the switch Sw₂ are l₁ = 11 and l₂ = 12, respectively. Thus, according to (9), the two transition probabilities are updated as $P_{\mathrm{0,1}}={\displaystyle \frac{11}{11+12}}=$ 0.47526 and $P_{\mathrm{0,2}}={\displaystyle \frac{12}{11+12}}=$ 0.52174.

To determine the initial transition probabilities among other nodes (excluding node 0) in the SAN, the following rule is used. Let N_j denote the set of neighboring nodes for node j, $\left|{\mathit{N}}_j\right|$ denote the cardinality of N_j, and k represents a neighboring node of node j (i.e., $k\in$ N_j). The initial value of $P_{ik}$ is determined using (10).

$$P_{ik}={\displaystyle \frac{1}{\left|{\mathit{N}}_j\right|}}$$

(10)

4.3. Problem Statement

The objective of this study is to evaluate the utilization and average response time of each node in the example SAN as well as the overall response time. Another objective is to show the impact of the proposed utilization-driven strategy in enhancing the SAN performance, particularly, in terms of load balancing degree among all the nodes and average response time. In addition, the influences of two important parameters (adjustment step value s and selection window size w) on the effectiveness of the proposed performance enhancement strategy are investigated.

5. Experiments and Results

To illustrate the performance of the proposed utilization-driven strategy and the sensitivity of parameters (i.e., s and w), we analyze the average (ρ_avg) and standard deviation (ρ_std) of the utilization of all the switches in the example SAN provided in Section 4, the average (W_avg) and standard deviation (W_std) of response time of all the switches, as well as the overall mean response time W of the SAN.

In Section 5.1, the impact of step value s is investigated using s = 0.01 (Case 1), s = 0.05 (Case 2), and s = 0.07 (Case 3) assuming w = 0.02. In Section 5.2, the impact of the selection window size w is examined using w = 0.02 (Case 3), w = 0.1 (Case 4), and w = 0.2 (Case 5) assuming s = 0.07.

As mentioned in Section 3, the threshold ρ* = 0.8 is used for triggering the traffic redistribution during the entire mission in all the analyses. Note that in the experiments, the traffic arrival rate λ increases in steps of 0.01. Redistribution is triggered when any switch’s utilization first exceeds the threshold ρ* = 0.8. Due to rounding, the value of λ is recorded as the last value before the threshold is crossed. For example, the utilization of a switch reaches 0.799946 at λ = 3.13 and exceeds the threshold (0.802) at λ = 3.14; thus, redistribution is triggered and implemented at λ = 3.13. All the metrics are evaluated using the JQN method described in Section 2 and switch service rate parameters in Table 1. The service rate of the servers (Sr₁ and Sr₂) and storage arrays (Sa₁ and Sa₂) used in the experiments is 16 Gb/s. Results are collected for three traffic redistributions applied to the example SAN system.

5.1. Effects of Adjustment Step Value s

Assuming w = 0.02, we conduct three experiments with different values of the transition probability adjustment step parameter s to study its impact on the effectiveness of the proposed utilization-driven performance enhancement strategy. Specifically, performance results under s = 0.01 (Case 1), s = 0.05 (Case 2), and s = 0.07 (Case 3) are collected and compared, as detailed below.

5.1.1. Case 1: w = 0.02 and s = 0.01

Figure 3 illustrates the utilization of each switch in the example SAN as the arrival rate to node 0 (i.e., λ) increases.

Table 2. Utilization of all switches, ρ_avg and ρ_std under s = 0.01 and w = 0.02.

Redistribution	First		Second		Third
λ	2.98		3.13		3.25
	before	after	before	after	before	after
Sw1	0.799188	0.746299	0.783991	0.762454	0.791779	0.775559
Sw2	0.798649	0.761487	0.799946	0.768714	0.798280	0.782550
Sw3	0.352123	0.347071	0.364601	0.365864	0.379936	0.385192
Sw4	0.712482	0.712791	0.748791	0.754322	0.783335	0.771306
Sw5	0.405723	0.410676	0.431418	0.424570	0.440899	0.447452
ρavg	0.613633	0.595665	0.625749	0.615185	0.638846	0.632412
ρstd	0.194960	0.178844	0.187877	0.180618	0.187565	0.177568

presents the utilization of each switch before and after each redistribution. During each redistribution, all nodes with utilization between 0.78 (ρ*-w) and 0.8 (ρ*) are chosen for transition probability adjustment. Specifically, in the first and second redistributions, Sw₁ and Sw₂ are selected; in the third redistribution, Sw₁, Sw₂, and Sw₄ are selected (highlighted in Table 2 and

Table 3. Response time of all switches, W_avg, W_std and W under s = 0.01 and w = 0.02.

Redistribution	First		Second		Third
λ	2.98		3.13		3.25
	before	after	before	after	before	after
Sw1	0.311236	0.246353	0.28934	0.263107	0.300162	0.27847
Sw2	0.248323	0.209632	0.249932	0.216183	0.247869	0.229938
Sw3	0.061740	0.061262	0.062952	0.063078	0.064509	0.065061
Sw4	0.193225	0.193433	0.221152	0.226132	0.256412	0.242926
Sw5	0.056091	0.056562	0.058625	0.057928	0.05962	0.060327
Wavg	0.174123	0.153449	0.176401	0.165285	0.185714	0.175344
Wstd	0.101225	0.079085	0.096857	0.086987	0.102518	0.093353
W	4.6612	4.0329	4.5674	4.2172	4.6780	4.3893

). The first redistribution is triggered at λ = 2.98 when the utilization of Sw₁ reaches the threshold ρ* = 0.8, the second redistribution is triggered at λ = 3.13 when the utilization of Sw₂ reaches the threshold, and the third redistribution occurs at λ = 3.25 when the utilization of Sw₂ reaches the threshold ρ* = 0.8. Table 2 also summarizes the values of ρ_avg and ρ_std before and after each redistribution. Figure 4 illustrates the average response time $W_j$ of each switch Sw_j and the overall response time W as λ increases. Table 3 summarizes the average response time of each switch before and after each redistribution, as well as the values of W_avg and W_std.

The decrease in ρ_std and W_std after each redistribution demonstrates that the proposed strategy can make the load of different switches more balanced. The decrease in W_avg (faster response times) and the overall response time W after each redistribution demonstrates the advantage of the proposed strategy in reducing the latency. By redistributing the load, the proposed strategy prevents certain switches from becoming overwhelmed while others are under-utilized. The adjustments help ensure a more uniform distribution of workload across the system, improving overall performance and utilization efficiency.

5.1.2. Case 2: w = 0.02 and s = 0.05

Similar to the analysis in Section 5.1.1, Figure 5 and Figure 6 illustrate the utilization and average response time of each switch in the example SAN as λ increases. Figure 6 also illustrates the overall response time W of the example SAN as λ increases.

Table 4. Utilization of all switches, ρ_avg and ρ_std under s = 0.05 and w = 0.02.

Redistribution	First		Second		Third
λ	2.98		3.29		3.50
	before	after	before	after	before	after
Sw1	0.799187	0.614231	0.678343	0.608058	0.646989	0.775742
Sw2	0.798649	0.637256	0.703771	0.632921	0.673444	0.778516
Sw3	0.352123	0.340244	0.375758	0.396116	0.421478	0.465316
Sw4	0.712481	0.724201	0.79979	0.750534	0.798586	0.715498
Sw5	0.405723	0.406378	0.448795	0.476845	0.507374	0.544798
ρavg	0.613633	0.544462	0.601291	0.572895	0.609574	0.655974
ρstd	0.194959	0.145984	0.161221	0.123993	0.131932	0.127761

presents the utilization of each switch as well as the values of ρ_avg and ρ_std before and after each redistribution.

Table 5. Average response time of all switches, W_avg, W_std and W under s = 0.05 and w = 0.02.

Redistribution	First		Second		Third
λ	2.98		3.29		3.50
	before	after	before	after	before	after
Sw1	0.311235	0.162014	0.194306	0.159462	0.177048	0.278697
Sw2	0.248323	0.137838	0.168788	0.136211	0.153113	0.22575
Sw3	0.061740	0.060628	0.064078	0.066238	0.069142	0.074811
Sw4	0.193224	0.201435	0.277487	0.222698	0.275828	0.195273
Sw5	0.056091	0.056153	0.060474	0.063716	0.067665	0.073228
Wavg	0.101224	0.057011	0.082366	0.05993	0.077306	0.082446
Wstd	0.174123	0.123614	0.153027	0.129665	0.148559	0.169552
W	4.6612	3.0654	3.7034	3.0559	3.4440	4.0638

summarizes the average response time of each switch as well as the values of W_avg and W_std before and after each redistribution.

During each redistribution, all nodes with utilization between ρ*-w = 0.78 and ρ* = 0.8 are chosen for transition probability adjustment. Specifically, in the first redistribution, Sw₁ and Sw₂ are selected; in the second and third redistributions, Sw₄ is selected (highlighted in Table 4 and Table 5). The first redistribution is triggered at λ = 2.98 when the utilization of Sw₁ reaches the threshold ρ*, the second redistribution is triggered at λ = 3.29 and the third redistribution occurs at λ = 3.50 when the utilization of Sw₄ reaches the threshold ρ*.

Like Case 1, the decrease in ρ_std following each redistribution indicates that the proposed strategy effectively balances the load across different switches. The decrease in W_avg and W following the first two redistributions demonstrates the strategy’s ability to reduce latency when the overall load remains low. However, the situation changes at the third redistribution when the external arrival rate λ reaches 3.5. At this point, ρ_avg, W_avg and W all increase due to the higher overall load, which causes each switch to become more heavily utilized. As the system becomes more saturated, each switch handles more traffic, causing increased contention for the resource and thus longer response times.

5.1.3. Case 3: w = 0.02 and s = 0.07

Similar to the previous analysis, Figure 7 and Figure 8 depict the utilization and average response time of each switch in the example SAN as the external arrival rate λ increases. Figure 8 also illustrates the overall response time W of the example SAN as λ increases.

Table 6. Utilization of all switches, ρ_avg and ρ_std under s = 0.07 and w = 0.02.

Redistribution	First		Second		Third
λ	2.98		3.26		3.4
ρ	before	after	before	after	before	after
Sw1	0.799188	0.554985	0.607306	0.762734	0.79559	0.556714
Sw2	0.798649	0.581239	0.636036	0.765772	0.798759	0.573061
Sw3	0.352123	0.337012	0.368784	0.42097	0.439104	0.414703
Sw4	0.712482	0.729613	0.798399	0.696212	0.726203	0.772203
Sw5	0.405723	0.404333	0.442452	0.490278	0.511397	0.490815
ρavg	0.613633	0.521436	0.570595	0.627193	0.654211	0.561499
ρstd	0.19496	0.138395	0.151442	0.143954	0.150155	0.119246

presents the utilization of each switch as well as the values of ρ_avg and ρ_std before and after each redistribution.

Table 7. Average response time of all switches, W_avg, W_std and W under s = 0.07 and w = 0.02.

Redistribution	First		Second		Third
λ	2.98		3.26		3.4
Wj	before	after	before	after	before	after
Sw1	0.311236	0.140445	0.159157	0.263417	0.305758	0.140993
Sw2	0.248323	0.119402	0.137376	0.213468	0.248459	0.117113
Sw3	0.061740	0.060333	0.063370	0.069081	0.071314	0.068341
Sw4	0.193225	0.205467	0.275571	0.182876	0.202908	0.243881
Sw5	0.056091	0.055960	0.059786	0.065395	0.068222	0.065464
Wavg	0.174123	0.116321	0.139052	0.158847	0.179332	0.127158
Wstd	0.101225	0.055347	0.078811	0.079104	0.095217	0.065088
W	4.6612	2.8168	3.3074	3.9541	4.3962	2.7690

summarizes the average response time of each switch as well as the values of W_avg and W_std before and after each redistribution.

In the first and third redistributions, Sw₁ and Sw₂ are selected; in the second redistribution, Sw₄ is selected (highlighted in Table 6 and Table 7). The first redistribution is triggered at λ = 2.98 when the utilization of Sw₁ reaches the threshold ρ* = 0.8, the second redistribution is triggered at λ = 3.26 when the utilization of Sw₄ reaches the threshold ρ*, and the third redistribution occurs at λ = 3.40 when the utilization of Sw₂ reaches the threshold ρ*.

Consistent with previous cases, the decrease in ρ_std following each redistribution indicates that the proposed strategy effectively balances the load across different switches. The reduction in W_avg, W_std and W following the first redistribution demonstrates the strategy’s effectiveness in reducing latency. However, at the second redistribution (λ = 3.26), an increase in ρ_avg correlates with rising values of W_avg, W_std, and W implying that the switches become more heavily utilized since the first redistribution. As the external arrival rate λ increases further, the third redistribution becomes effective again in reducing W_avg, W_std and W. This can be attributed to the fact that the redistribution process can effectively minimize bottlenecks, reducing traffic at heavily loaded switches. Moreover, as more redistributions are conducted, load is more evenly distributed, resulting in less fluctuation in utilization and response times.

5.1.4. Summary of Effects of Adjustment Step Value s

Table 8. IR of ρ_std. W_std and W at each redistribution under different values of parameter s.

ρstd
s	First	Second	Third	Average
0.01	−0.0827	−0.0386	−0.0533	−0.0582
0.05	−0.2512	−0.2309	−0.0316	−0.1712
0.07	−0.2901	−0.0495	−0.2059	−0.1818
Wstd
s	First	Second	Third	Average
0.01	−0.2187	−0.1019	−0.0894	−0.1367
0.05	−0.4368	−0.2724	0.0665	−0.2142
0.07	−0.4532	0.0037	−0.3164	−0.2553
W
s	First	Second	Third	Average
0.01	−0.1348	−0.0767	−0.0617	−0.0911
0.05	−0.3424	−0.1748	0.1800	−0.1124
0.07	−0.3957	0.1955	−0.3701	−0.1900

summarizes the improvement ratio at each redistribution for ρ_std, W_std and W under different values of the transition probability adjustment step parameter s. The improvement ratio (IR) is defined in (11), where A and B denote the performance metric after and before the redistribution, respectively. The average IR (as shown in the last column of Table 8) is calculated based on the IR values in the three redistributions. For all the three performance metrics ρ_std, W_std and W, the smaller their values, the better the performance of the SAN system or the proposed strategy. Therefore, the improvements are indicated by negative values of IR.

$$IR={\displaystyle \frac{A-B}{B}}$$

(11)

As the value of s increases, the absolute values of the average IR all increase for ρ_std. W_std and W, implying that the proposed utilization-driven strategies become more effective in achieving load balance and in reducing response times.

5.2. Effects of Selection Window Size w

Assuming s = 0.07, we conduct two more experiments with w = 0.1 (Case 4) and w = 0.2 (Case 5). Together with Case 3 studied in Section 5.1.2 where w = 0.02, we study the impact of the selection window size w on the effectiveness of the proposed utilization-driven performance enhancement strategy.

5.2.1. Case 4: s = 0.07 and w = 0.1

Figure 9 and Figure 10 illustrate the utilization and average response time of each switch in the example SAN as the external arrival rate λ increases. Figure 10 also illustrates the overall response time W of the example SAN as λ increases.

Table 9. Utilization of all switches, ρ_avg and ρ_std under s = 0.07 and w = 0.1.

Redistribution	First		Second		Third
λ	2.98		3.42		3.89
	before	after	before	after	before	after
Sw1	0.799188	0.681535	0.782504	0.689241	0.784239	0.697394
Sw2	0.798649	0.695682	0.798746	0.701763	0.798487	0.70243
Sw3	0.352123	0.380847	0.437269	0.464034	0.527992	0.549905
Sw4	0.712482	0.634236	0.728197	0.660232	0.751231	0.690172
Sw5	0.405723	0.454048	0.521315	0.561399	0.638777	0.677011
ρavg	0.613633	0.56927	0.653606	0.615334	0.700145	0.663382
ρstd	0.194960	0.127737	0.146661	0.090276	0.102718	0.05738

presents the utilization of each switch as well as the values of ρ_avg and ρ_std before and after each redistribution.

Table 10. Average response time of all switches, W_avg, W_std and W under s = 0.07 and w = 0.1.

Redistribution	First		Second		Third
λ	2.98		4.29		5.85
	before	after	before	after	before	after
Sw1	0.311236	0.196254	0.287361	0.201120	0.289672	0.206539
Sw2	0.248323	0.164302	0.248443	0.167652	0.248123	0.168028
Sw3	0.061740	0.064604	0.074632	0.060085	0.084744	0.088870
Sw4	0.193225	0.151889	0.204397	0.163510	0.223322	0.179311
Sw5	0.056091	0.061055	0.069635	0.075999	0.092279	0.103203
Wavg	0.174123	0.127621	0.176893	0.133673	0.187628	0.149190
Wstd	0.101225	0.054858	0.089488	0.055381	0.083694	0.045397
W	4.6612	3.2605	4.3159	3.2683	4.2874	3.4054

summarizes the average response time of each switch as well as the values of W_avg, W_std and W before and after each redistribution.

During each redistribution, all nodes with utilization between ρ* − w = 0.7 and ρ* = 0.8 are chosen for transition probability adjustment. In all the three redistributions, Sw₁, Sw₂ and Sw₄ are selected (highlighted in Table 9 and Table 10). The first redistribution is triggered at λ = 2.98 when the utilization of Sw₁ reaches the threshold ρ* = 0.8, the second redistribution is triggered at λ = 3.42 and the third redistribution occurs at λ = 3.89 when the utilization of Sw₂ reaches the threshold ρ*.

Like Case 1, ρ_avg, ρ_std, W_avg, W_std and W all decrease after each redistribution, confirming that the proposed strategy effectively balances the load across different switches and improves overall response time and utilization efficiency.

5.2.2. Case 5: s = 0.07 and w = 0.2

Figure 11 and Figure 12 illustrate the utilization and average response time of each switch in the example SAN as the external arrival rate λ increases. Figure 12 also illustrates the overall response time W of the example SAN as λ increases.

Table 11. Utilization of all switches, ρ_avg and ρ_std under s = 0.07 and w = 0.2.

Redistribution	First		Second		Third
λ	2.98		3.42		3.89
	before	after	before	after	before	after
Sw1	0.799188	0.681535	0.782504	0.689241	0.784239	0.734402
Sw2	0.798649	0.695682	0.798746	0.701763	0.798487	0.723097
Sw3	0.352123	0.380847	0.437269	0.464034	0.527992	0.611864
Sw4	0.712482	0.634236	0.728197	0.660232	0.751231	0.717596
Sw5	0.405723	0.454048	0.521315	0.561399	0.638777	0.585046
ρavg	0.613633	0.569270	0.653606	0.615334	0.700145	0.674401
ρstd	0.194960	0.127737	0.146661	0.090276	0.102718	0.062821

presents the utilization of each switch as well as the values of ρ_avg and ρ_std before and after each redistribution.

Table 12. Average response time of all switches, W_avg, W_std and W under s = 0.07 and w = 0.2.

Redistribution	First		Second		Third
λ	2.98		3.42		3.89
	before	after	before	after	before	after
Sw1	0.311236	0.196254	0.287361	0.201120	0.289672	0.235318
Sw2	0.248323	0.164302	0.248443	0.167652	0.248123	0.180568
Sw3	0.061740	0.064604	0.074632	0.060085	0.084744	0.103057
Sw4	0.193225	0.151889	0.204397	0.163510	0.223322	0.196724
Sw5	0.056091	0.061055	0.069635	0.075999	0.092279	0.080330
Wavg	0.174123	0.127621	0.176893	0.133673	0.187628	0.159199
Wstd	0.101225	0.054858	0.089488	0.055381	0.083694	0.058363
W	4.6612	3.2605	4.3159	3.2683	4.2874	3.5538

summarizes the average response time of each switch as well as the values of W_avg, W_std, and W before and after each redistribution.

Nodes with utilization between ρ*-w = 0.6 and ρ* = 0.8 are selected for transition probability adjustment during each redistribution. In the first two redistributions, Sw₁, Sw₂, and Sw₄ are selected for adjustment, while in the third redistribution, Sw₅ is additionally included (highlighted in Table 11 and Table 12). The three redistributions are triggered at λ = 2.98, λ = 3.42, and λ = 3.89, respectively.

Consistent with Case 4, the decrease in ρ_avg, ρ_std, W_avg, W_std and W after each redistribution confirms the effectiveness of the proposed strategy in load balancing and improving the overall response time and utilization efficiency.

5.2.3. Summary of Effects of Selection Window Size

Table 13. IR of ρ_std. W_std and W under different values of w.

ρstd
w	First	Second	Third	Average
0.02	−0.2901	−0.0495	−0.2059	−0.1818
0.1	−0.3448	−0.3845	−0.4414	−0.3902
0.2	−0.3448	−0.3845	−0.3884	−0.3726
Wstd
w	First	Second	Third	Average
0.02	−0.4532	0.0037	−0.3164	−0.2553
0.1	−0.4581	−0.3811	−0.4576	−0.4323
0.2	−0.4581	−0.3811	−0.3027	−0.3806
W
w	First	Second	Third	Average
0.02	−0.3957	0.1955	−0.3701	−0.1900
0.1	−0.3005	−0.2427	−0.2057	−0.2497
0.2	−0.3005	−0.2427	−0.1711	−0.2381

summarizes the improvement ratio IR, evaluated using (11), at each redistribution for ρ_std, W_std and W under different values of selection window size parameter w. As w increases from 0.02 to 0.1, the absolute values of average IR of ρ_std, W_std and W increase. However, as w increases further, the absolute values of average IR of those three metrics decrease. This can be explained by the fact that in the case of a large selection window, more nodes (particularly, more than majority of nodes in the example SAN) are involved in the redistribution process, which potentially reduces the degree of adjustment for highly utilized nodes. This implies that the proposed utilization-driven strategies are more effective in achieving load balancing and reducing response times when the selection window size is not overly aggressive, i.e., not involving more than the majority of nodes. Note that the identical results in the first two redistributions for w = 0.1 and w = 0.2 are due to the involvement of the same set of switches for traffic redistribution.

6. Conclusions and Future Work

This paper contributes by proposing a utilization-driven traffic redistribution strategy to enhance the performance of SAN systems. A JQN-based method is adapted to assess the utilization and response time of switches as well as the overall response time of the SAN system. The effectiveness of the proposed strategy in balancing load across switches and in improving average response times is demonstrated using a detailed case study of a mesh SAN system. The impacts of adjustment step parameter s and selection window size w on the effectiveness of the proposed performance enhancement strategy are also investigated using case studies.

The following has been revealed: (1) The proposed dynamic traffic redistribution process ensures a more uniform workload distribution and reduces the likelihood of forming bottlenecks and causing cascading failures. As a result, overall response time and utilization efficiency can be improved. (2) A larger adjustment step tends to result in higher average improvements in both utilization and response times, as well as more balanced load across SAN switches. (3) The selection window size should be carefully designed to allow for more effective adjustments to heavily loaded nodes.

The proposed model assumes that the key parameters like adjustment step parameter s and node selection window size w remain constant during the mission. One future direction could focus on investigating adaptive methods to dynamically adjust these two parameters in response to changing traffic conditions and switch failures. Moreover, other factors like real network latency and jitter as well as hardware constraints will be considered. While this work has demonstrated the effectiveness of the proposed strategy in a mesh SAN system, further research could investigate the scalability of the proposed method in larger and more complex SAN systems. Another potential direction for future research is to integrate machine learning methods that could help predict future loads for proactive load planning and further enhancing SAN performance [33]. We are also interested in exploring online optimization algorithms [34] for reducing the service response time and overall energy consumption. Additionally, to further strengthen the practical significance of the proposed work, pursuing real-world implementation and validation would be another valuable direction for future work. The operational overhead and challenges associated with deploying the method in practice will be assessed.