Ballooning Graphics Memory Space in Full GPU Virtualization Environments

Advances in virtualization technology have enabled multiple virtual machines (VMs) to share resources in a physical machine (PM). With the widespread use of graphics-intensive applications, such as two-dimensional (2D) or 3D rendering, many graphics processing unit (GPU) virtualization solutions have been proposed to provide high-performance GPU services in a virtualized environment. Although elasticity is one of the major benefits in this environment, the allocation of GPU memory is still static in the sense that after the GPU memory is allocated to a VM, it is not possible to change the memory size at runtime. This causes underutilization of GPU memory or performance degradation of a GPU application due to the lack of GPU memory when an application requires a large amount of GPU memory. In this paper, we propose a GPU memory ballooning solution called gBalloon that dynamically adjusts the GPU memory size at runtime according to the GPU memory requirement of each VM and the GPU memory sharing overhead. The gBalloon extends the GPU memory size of a VM by detecting performance degradation due to the lack of GPU memory. The gBalloon also reduces the GPU memory size when the overcommitted or underutilized GPU memory of a VM creates additional overhead for the GPU context switch or the CPU load due to GPU memory sharing among the VMs. We implemented the gBalloon by modifying the gVirt, a full GPU virtualization solution for Intel’s integrated GPUs. Benchmarking results show that the gBalloon dynamically adjusts the GPU memory size at runtime, which improves the performance by up to 8% against the gVirt with 384 MB of high global graphics memory and 32% against the gVirt with 1024 MB of high global graphics memory.


Introduction
Running graphics-intensive applications that include threedimensional (3D) visualization and rendering in a virtualized environment creates a new challenge for highperformance graphics processing unit (GPU) virtualization solutions. GPU virtualization is a technique that allows multiple virtual machines (VMs) to share a physical GPU and run high-performance graphics applications with performance guarantees.
is method is easy to implement, but requires modification every time the version of the API library or GPU driver changes. is method also cannot provide all GPU functions. Direct pass-through [12,13] allocates a GPU exclusively to a single VM and allows it to directly use the GPU with no intervention by the hypervisor. is method provides a high performance that is similar to the native environment, but GPU sharing among VMs is impossible. Currently, AWS [14] and Azure [15] provide GPU services to VMs through the direct pass-through method or through the NVIDIA GRID [16] which is a GPU virtualization solution at the hardware level.
To solve the problems of the approaches mentioned above, GPU virtualization solutions at the hypervisor level, such as gVirt [17], GPUvm [18], and VMCG [19], have been proposed. e gVirt is a full GPU virtualization technology for Intel's integrated GPUs. Unlike dedicated or discrete GPUs in which dedicated graphic cards have independent graphics memory, integrated GPUs share a portion of the system RAM for graphics memory (or GPU memory). e original gVirt divides the graphics memory into chunks and allocates them exclusively to each VM. As a result, a single host could create up to only a maximum of three VMs. e gScale [20,21] solved this scalability problem by dividing the graphics memory into multiple small slots and letting VMs share the slots. Private and physical graphics translation tables (GTTs) are used to translate the virtual address generated by each VM into the physical address for the graphics memory. When a VM is scheduled to run, the private GTT entries of the corresponding VM are copied to the physical GTT. Every time entries are updated in the physical GTT, the modified contents are synchronized with the private GTT that each VM has.
However, the GPU memory size, which is set during the initial creation of the VM, cannot be changed dynamically.
is causes the following problems. First, a VM must be restarted to change the allocated GPU memory size. e user must restart the VM to execute the GPU application that requires GPU memory larger than the current setting. As a result, the VM stops, and the service interruption is expectable. Second, the VM that occupies GPU memory larger than necessary can degrade the performance of other CPU and GPU applications running on other VMs. Whenever a GPU context switch occurs, the CPU copies the private GTT entries to a physical GTT, which also takes up the CPU time of other VMs. If the memory utilization is low, this unnecessary copying overhead may degrade the performance of other VMs. In addition, the GPU context switch time increases as the GPU memory size of each VM gets larger [22]. ird, as we reported in a previous study [22], small GPU memory size affects the performance of GPU workload, especially when VMs run with graphics operations for rendering or high-resolution display environments.
Although several studies [23][24][25][26][27][28][29] dynamically adjusted the memory allocation of existing VMs, in these studies, memory was taken from a specific VM and allocated to another VM when the physical memory was insufficient. As these approaches assume an environment in which each VM has an independent virtual address space, it is difficult to apply those techniques directly to the full GPU virtualization environment in which the same virtual GPU memory space is shared.
In this paper, we propose a dynamic GPU memory ballooning scheme called gBalloon which dynamically increases or decreases the GPU memory size allocated to each VM at runtime. e gBalloon detects performance degradation due to the lack of GPU memory and increases the GPU memory size allocated to each VM. In addition, the GPU memory size of each VM can be reduced when the overcommitted or underutilized GPU memory of a VM creates additional overhead for the GPU context switch or the CPU load due to GPU memory sharing among the VMs. We implement the gBalloon using the 2016Q4 version of gVirt. As the gScale's GPU memory-sharing technique is also implemented, the gBalloon can scale up to 15 Linux VMs. Using various CPU and GPU benchmarks, we also show that the gBalloon dynamically adjusts the GPU memory size at runtime and outperforms the gVirt (modified gVirt in which the gScale's features are added) by up to 8% against the gVirt with 384 MB of high global graphics memory and 32% against the gVirt with 1024 MB of high global graphics memory.
Although current gBalloon is mainly targeted at Intel's integrated GPU, its design principle can be applied to other architectures as well. For example, the proposed idea can be easily applied to other integrated GPUs from AMD and Samsung, where the system memory is used as GPU memory. In addition, we believe that other discrete GPUs with dedicated memory such as NVIDIA can benefit from the gBalloon since they also use graphics translation table for address translation. However, special care has to be taken to reduce the memory copy overhead across the system bus if the gBalloon is implemented over discrete GPUs. As the gVirt is open source and the access to the source codes for the NVIDIA driver and runtime is limited, we decided to use the gVirt as a software platform to verify our proposed idea. e rest of the paper is organized as follows. In Section 2, we outline the structure of gVirt and present the motivations behind the design of gBalloon. In Section 3, we explain the design and implementation issues of gBalloon. In Section 4, we evaluate the performance of gBalloon and compare it with that of gVirt using various configurations. In Section 5, we discuss related works, and in Section 6, we conclude with suggestions for future work.

Background and Motivation
In this section, we provide an overview of the gVirt and discuss the motivations for the proposed approach.

Overview of gVirt.
e gVirt is a high-performance GPU virtualization solution that provides mediated pass-through capability [17]. e gVirt allows VMs to directly access resources that have a large effect on performance and make other privileged operations be intervened through a hypervisor. Due to the restriction on the number of simultaneous VMs in the gVirt, we modified the original gVirt over Xen hypervisor (XenGT) and added the gScale's scalability features [20]. roughout this paper, we consider the modified gVirt as gVirt.
In the gVirt, the mediator located in Dom0 emulates the virtual GPU (vGPU) for each VM. e mediator schedules the vGPU in a round-robin fashion for fair scheduling among the VMs. Considering the high cost of the GPU context switch, each vGPU is switched at approximately 16 ms interval, which is a speed at which people cannot recognize an image change [17]. When the time quantum allocated to each vGPU is fully used, the mediator saves the registers and memory information of the corresponding vGPU and restores the GPU state for the next vGPU. Because the gVirt does not support preemption (although NVIDIA starts to provide preemption capability at the hardware level from Pascal architecture, the feature is not exposed to user's control at the time of this writing) at the time of this writing, it traces the submitted GPU commands and waits for the results until each vGPU can finish its jobs.
For example, if a vGPU executes GPU kernels longer than 16 ms, it runs without preemption. To prevent each vGPU from overusing the time quantum, the gVirt places a limit on the number of GPU kernels a vGPU is allowed to run within the time quantum.
Intel's global graphics memory is divided into two parts as shown in Figure 1: low global graphics memory and high global graphics memory. Only the GPU can access high global graphics memory, but the CPU and the GPU can access low global graphics memory. e CPU can access low global graphics memory through the aperture mapped to the GPU memory.
us, the amount of low global graphics memory that can be accessed depends on the aperture size. e maximum aperture size currently supported by the motherboard is 512 kB, which is mapped up to 512 MB of the low global graphics memory. Figure 1 shows the memory mapping and management structure between global graphics memory and system memory. In the gVirt (modi ed gVirt in which the gScale's features are added), part of the low global graphics memory is shared by all vGPUs, and the high global graphics memory is divided into 64 MB slots that can also be shared among the vGPUs. e virtual address of the global graphics memory is converted into a physical address through the physical GTT. Each vGPU has a private GTT, which is a copy of the physical GTT corresponding to the allocated low global graphics memory and high global graphics memory. e private GTT entries of the vGPU are synchronized every time each vGPU modi es the physical GTT entries. To activate the vGPU in a GPU context switch, if the entry does not exist in the physical GTT, the state is restored by copying the private GTT to the physical GTT. However, if the vGPU is scheduled out, the CPU cannot access the vGPU through aperture. To solve this problem, the gScale allows the CPU to access the vGPU space at all times through the fence memory space pool, which ensures the proper operation of ladder mapping for mapping the guest physical address to the host physical address [20]. e gVirt framework focuses on the acceleration of graphics-intensive applications such as 2D or 3D rendering over a virtualized environment, rather than general-purpose computing on graphics processing units (GPGPU) computing over clouds.

Motivation.
In current gVirt, 64 MB low global graphics memory and 384 MB high global graphics memory are recommended for Linux VM [20] because those memory sizes are enough to support most GPU workloads without performance degradation and crash from the experiments. However, we showed in a previous study [22] that large high global graphics memory can sometimes increase the performance of GPU workloads. We also observed in the study that large high global graphics memory can increase the possibility of overlapping address spaces, which may incur large overhead in a GPU context switch and thus degrade the performance of other VMs. Furthermore, in an environment where the VMs require large global graphics memory, it is highly likely that their GTT entries do not exist in the physical GTT in a GPU context switch because the GPU memory space is shared among the VMs. If a large amount of GPU memory is allocated although it is not fully utilized, unnecessary copies of the GTT entries can occur in a GPU context switch. is increases the time for the GPU context switch, which also decreases the time for each vGPU to occupy the GPU per unit time. As a result, not only the performance of the GPU applications running on all VMs is degraded but also the time for the CPU to copy the GTT entries increases. erefore, the performance of the CPU applications running on the VMs can be degraded as well.
To con rm this, we conducted two experiments to investigate the e ects of copying GTT entries on the performance of GPU application due to excessive occupation of high global graphics memory. For the two experiments, 384 MB and 1024 MB are used for the high global graphics memory size. It is possible to use other con gurations as long as it is bigger than 384 MB and smaller than the size of physical GPU memory. Furthermore, the size should be multiple of slot size. Figure 2 shows the sum of the frames per second (FPS) for each VM by executing Nexuiz 3D benchmarks from Phoronix Test Suite [30] as we increase the number of VMs from 3 to 15. As shown in Figure 2, when the size of the high global graphics memory is small (384 MB), the VMs start to share the GPU memory from the point when the number of VMs reaches around 10. en, the performance of the VMs degrades as we increase the number of VMs to 12 or 15. However, when the size of the high global graphics memory is large (1024 MB), the VMs start to share GPU memory from the relatively small number of VMs. is means that the copying of the GTT entries in the GPU context switch causes a very large performance degradation. When the number of VMs is 6 or 9, the performance at 1024 MB degraded by approximately 3.5 times compared with the performance at 384 MB.
Overall, the performance of the VMs is highly a ected by the size of the GPU memory allocated to each VM, and the memory size must be adjusted at runtime to optimize the performance.

Design of gBalloon
In this section, we describe the design and implementation of the gBalloon that adjusts the GPU memory size of VMs at runtime. As we identi ed in the previous section, the performance of a GPU application can be degraded due to the static allocation of GPU memory. e gBalloon monitors the lack of GPU memory in VMs and then allocates the required amount of GPU memory to the corresponding VM. Furthermore, the gBalloon also checks the performance of CPU and GPU applications and decreases the GPU memory size when the performance of each VM degrades due to the GPU memory sharing among the VMs. e gBalloon is implemented by modifying the gVirt 2016Q4 release [31]. In the following, we present the GPU memory expansion and reduction strategies implemented in the gBalloon in detail.

GPU Memory Expansion Strategy.
When a VM is created, the GPU driver of the VM obtains the available range of GPU memory from the GPU driver in Dom0 and balloons the requested memory area excluding the space that has been allocated to the VM. en, the GPU driver of the VM searches for memory space excluding the ballooned area when allocating a new memory object. If the space for allocating an object is insu cient, the GPU driver creates an empty space by returning the existing memory objects. As a result, the performance of a GPU application that requires graphics-intensive operations, such as rendering operations, is degraded because the same objects are frequently returned. To reduce this overhead, the gBalloon detects the VMs' lack of GPU memory by tracing the number of memory object returns at runtime and reduces the ballooned area of other VMs for the required amount of memory space so that the VM with the lack of memory can use additional GPU memory. Figure 3 shows the process in which the gBalloon allocates additional GPU memory to the guest. When a guest GPU driver must return an existing object due to the lack of GPU memory, the following four steps take place.
Step 1: the guest requests additional GPU memory space from the host.
Step 2: to expand the GPU memory space with the requested size, the host chooses the optimal strategy that can minimize the GPU memory-sharing overhead based on the GPU memory adjustment algorithm which will be explained later.
Step 3: based on the results of the GPU memory adjustment algorithm, the size of the guest's private GTT is increased.
Step 4: nally, the guest receives information about the GPU memory expansion from the host and shrinks the existing ballooned area so that it can be used to allocate objects. For example, as shown in Figure 3, the high global graphics memory area of vGPU1 is expanded to the right, and the shared memory areas of vGPU1 and vGPU3 are increased accordingly.

GPU Memory Reduction Strategy.
As the GPU memory is expanded by the GPU memory expansion request of a VM, the size of the GPU memory shared among the VMs can also be increased. Consequently, the probability that the entry will not exist in the physical GTT during the GPU context switch is increased, resulting in more GTT entry copies. is degrades the performance of the GPU application. In addition, as the number of entries to be copied is also increased, the CPU consumes more time copying the GTT entries, thus degrading the performance of the CPU application.
e gBalloon monitors the CPU cycles consumed for copying GTTentries during the GPU context switch to check the performance degradation of the GPU application. Pro ling is performed at every t cycles. When N is the number of CPUs in the host and C is the CPU cycles consumed for copying GTT entries, the rate of time R copy consumed by the CPU to copy the GTTentries for unit time t can be expressed as follows: Because one CPU processes the copying of the GTT entries, a total of N CPUs consume the cycles for the unit time. us, the number of CPUs must be re ected in R copy .
To check the performance degradation of the CPU application due to the competition among the vCPUs, the gBalloon uses the steal time. e steal time is the time when the vCPU of a VM exists in the ready queue. Assume that w ij is the steal time of the vCPU j of VM i and s ij is the time when the vCPU j of VM i exists in other queues. en, the rate W of the steal times in all VMs can be expressed as follows: A large value of W means that there is severe competition among the VMs. erefore, the state of a physical machine (PM) can be de ned by the values of W and R copy . If both W and R copy are large, then the performance of the CPU application is being degraded by the copying of the GTT entries. In this case, the host must prevent the performance degradation of the CPU and GPU applications by rejecting the GPU memory expansion requests of the VMs and reducing the GPU memory sharing among the VMs. Whereas, if W is large, but R copy is small, although there is severe competition among the VMs, it is not caused by the copying of the GTT entries. In this case, the performance of the CPU application could be degraded due to the increase in R copy .
us, the GTTsize should be reduced if possible. However, if W is small, but R copy is large, there is no competition among the VMs, but many copies of the GTT entries are occurring. In this case, if the VMs perform CPU applications, then the competition among the vCPUs can become more severe due to the copies of the GTT entries, and thus, the performance of the CPU application can degrade. erefore, the host should try to reduce the sharing of GPU memory as much as possible. Finally, if both W and R copy are small, there is no overhead in the current PM, and the host does not need to take any action. Based on the implications described above, the gBalloon identi es the degree of overhead in the host using the values of W and R copy . f(W, R copy ), which represents the degree of overhead incurred due to the copying of the GTTentries, can be expressed as follows: where α and β are the reciprocals of maximum W and R copy . ose parameters normalize the overall value by giving the same weight to W and R copy . e maximum W and R copy are dependent upon a particular hardware platform and are generally determined through experiments.
e gBalloon calculates f(W, R copy ) every 0.5 seconds and classi es the value with two thresholds Threshold low and Threshold high . Based on the classi cation, the gBalloon applies di erent GPU memory policies. e threshold values are experimentally determined from 0 to 2 as the value of f(W, R copy ) ranges from 0 to 2. For the experiments, we use 0.5 (25% of the maximum value) and 1 (50% of the maximum value) for Threshold low and Threshold high , respectively. If f(W, R copy ) is smaller than Threshold low , the gBalloon approves all requests for GPU memory expansion and does not reduce the GPU memory of the VMs. If f(W, R copy ) is larger than Threshold low , the gBalloon starts to decrease the size of the GPU memory allocated to each VM to reduce the overhead of the GPU memory sharing among the VMs. Instead of reducing the GPU memory of all VMs, the gBalloon reduces the GPU memory of the VM that occupies a large amount of GPU memory and has the lowest GPU memory utilization. If f(W, R copy ) is larger than Threshold high , the gBalloon rejects all requests for GPU memory expansion from the VMs and reduces a space corresponding to two 64 MB slots regardless of the GPU memory usage of each VM. e method for reducing GPU memory is to minimize the GPU memory sharing by using Algorithm 1 described in the next subsection.

GPU Memory Adjustment Algorithm.
e GPU memory is adjusted to minimize the GPU memory sharing with the existing VMs. When the gBalloon decides the number of GPU memory slots and the target vGPU to adjust based on the GPU memory expansion and reduction strategies discussed earlier, the spaces at both sides of the GPU memory space allocated to VMs are increased or decreased.
For example, let us assume that vGPU4 initiated a GPU memory expansion request for two slots when there are four vGPUs from vGPU1 to vGPU4 that require two, two, two, and one slots, respectively. Also assume that there are ve slots, and the GPU memory size of the host is 320 MB as shown in Figure 4. In this case, there are three possible methods for expanding the two slots as requested by vGPU4: (1) expanding two slots to the left side, (2) expanding one slot each to the left and right sides, and (3) expanding two slots to the right side. In the rst case, vGPU4 shares slots 1 and 2 with vGPU1, resulting in two shared slots in total. In the second case, vGPU4 shares slot 2 with vGPU1 and slot 4 with vGPU2 and vGPU3, resulting in three shared slots in total. In the third case, vGPU4 shares slot 4 with vGPU2 and vGPU3 and slot 5 with vGPU3, resulting in three shared slots in total. erefore, a strategy of expanding two slots to the left minimizes the number of shared slots. e gBalloon measures the number of shared slots and expands the GPU memory allocated to the VM to minimize the sharing overhead among the VMs.  L, R: the number of slots to expand/reduce to the left side and the right side Lcount ⟵ the number of occupied slots from P K − i to P K − 1 by V j (7) Rcount ⟵ the number of occupied slots from P K + S K to P K + S K + Q − i − 1 by V j (8) count ⟵ count + Lcount + Rcount (9) end for (10) if minimum > count then (11) minimum ⟵ count; Lcount ⟵ the number of occupied slots from P K to P K + i − 1 by V j (8) Rcount ⟵ the number of occupied slots from P K + S K + i − Q to P K + S K − 1 by V j (9) count ⟵ count + Lcount + Rcount (10) end if (11) end for (12) if maximum < count then (13) maximum ⟵ count (14) L ⟵ i (15) end if (16)  e method for reducing GPU memory is the same as that for expanding it. In Figure 4, when the GPU memory of vGPU3 should be reduced by one slot, reducing slot 4 rather than slot 5 can minimize the GPU memory sharing among the VMs. us, the policy for minimizing the GPU memory sharing can maximize the effect of the predictive-copy technique [21] that copies the GTT entries in advance by predicting the next scheduled vGPU before the GPU context switch. e detailed algorithms for memory expansion and reduction are presented below.

Performance Evaluation
In this section, we compare the performance of the gBalloon with that of the gVirt using various workloads. Table 1 shows the experimental environment for the performance evaluation. e global graphics memory size of the host is set to 4 GB, which consists of 256 MB of low global graphics memory and 3840 MB of high global graphics memory. Dom0 does not share the global graphics memory with other domains, but other guest VMs share 64 MB of the low global graphics memory and 3456 MB of the high global graphics memory excluding the Dom0 area. e low global graphics memory size of every guest VM is set to 64 MB as recommended in [20], whereas the high global graphics memory size is set differently depending on the experiments. e experiments use four 3D benchmarks and four 2D benchmarks. To measure the 3D performance, Lightsmark, Openarena, Nexuiz, and Urbanterror of Phoronix Test Suite [30] and Unigine Valley (valley) [32] that requires many rendering operations are used. To measure the 2D performance, Firefox-asteroids (Firefox-ast), Firefox-scrolling (Firefox-scr), gnome-system-monitor (gnome), and Midori of Cairo-perf-trace [33] are used. e performance of the 3D benchmarks is measured by the average number of FPS, and the performance of the 2D benchmarks is measured by the execution time. Furthermore, the NAS Parallel Benchmark (NPB) [34] is used to measure the overhead for the CPU due to the GPU context switch.

Performance Comparison Using a Single GPU Application.
In this subsection, the performance of the gVirt and the gBalloon is compared when valley that requires many rendering operations is executed by multiple VMs. For the gVirt, the gVirt-384 (a gVirt version with the high global graphics memory set to 384 MB) and the gVirt-1024 (a gVirt version with the high global graphics memory set to 1024 MB) are used for the performance comparison. For the 2D and 3D benchmarks that do not demand many rendering operations, additional GPU memory is not allocated because they require a small amount of high global graphics memory. erefore, valley is used to compare the performance of the dynamic GPU memory expansion policy of the gBalloon with that of the gVirt. To observe the performance variations due to the increase in the number of VMs and the change in the degree of GPU memory sharing, experiments were performed in which the number of VMs was increased by three. Figure 5 depicts the performance of the gVirt-384, the gVirt-1024, and the gBalloon normalized to the performance of the gVirt-384 by the sum of the FPS values of all VMs when there are 3, 6, 9, 12, or 15 VMs. When the number of VMs is six or fewer, the gVirt-1024 shows better performance than the gVirt-384 because the overhead from the GPU memory sharing is small. e gBalloon also shows a similar performance as the gVirt-1024 because the gBalloon allocates the required amount of GPU memory to VMs. In particular, as the number of VMs is increased, the performance of the gVirt-1024 and the gBalloon becomes more similar because the effect of overhead on the performance degradation becomes small, and the effect of performance degradation due to the GPU memory sharing becomes large. For this reason, all implementations show similar performance when the number of VMs is nine or higher.

Performance Comparison Using Multiple GPU
Applications. In this subsection, the performance of gVirt-384, gVirt-1024, and gBalloon is compared by running various types of GPU applications on 15 VMs. As shown in Table 2, 15 VMs run randomly selected 2D and 3D benchmarks. Because various benchmarks are mixed, it is possible to compare the degree of the performance degradation of the GPU applications due to the GPU memorysharing overhead that may occur as the requirements for the GPU memory change. Figure 6 shows the performance comparison when the randomly selected 2D and 3D benchmarks shown in Table 2 are executed by 15 VMs. All performance values are normalized to that of the gVirt-384. Strangely, valley in the gVirt-1024 shows a better performance than the gVirt-384 although the overhead is large due to the GPU memory sharing. However, the performance of the other 3D benchmarks is decreased by 50% or higher and the performance of the 2D benchmarks by 25%.
us, the performance of the total VMs drops by 24%, on average, compared with that of the gVirt-384. In the case of the gBalloon, the performance of valley is guaranteed because the GPU memory size of each VM expands as the required amount of GPU memory increases. Moreover, the gBalloon minimizes the overhead due to the GPU memory sharing by dynamically adjusting the GPU memory size according to the GPU memory usage. As a result, the GPU context switch time is decreased, and the performance of valley is increased by up to 28%. e performance of the other benchmarks is similar to that of the gVirt-384. Figure 7 shows a summary of the performance in all benchmarks. e performance of the gBalloon is higher by 8% than that of the gVirt-384 and higher by 32% than that of the gVirt-1024.

Performance Comparison Using CPU and GPU
Applications. In this subsection, the effect of performance degradation in CPU applications caused by the copying of the private GTT entries is analyzed. Among the 15 VMs, 7 VMs run with CPU workloads, whereas the remaining 8 VMs run with GPU workloads. e CPU workload uses cg Scientific Programming of the NPB benchmark, which is a workload to nd the smallest eigenvalue of the matrix using the conjugate gradient method. Figure 8 shows the performance of the CPU and GPU benchmarks normalized to that of the gVirt-384. In the case of the gVirt-1024, the performance of cg is decreased by 19% compared with that of the gVirt-384. is is because the CPU consumes a great deal of time copying the private GTT entries due to the large amount of GPU memory shared among the VMs. Furthermore, the performance of valley is increased slightly by approximately 4% due to this overhead. In contrast, the gBalloon limits the increase in the GPU memory size of the VMs by detecting the overhead of the CPU and the overhead due to the copying of the GTT entries. As a result, the performance of cg is decreased by approximately 1.5%, and the performance of valley is increased by approximately 2% compared with that of gVirt-384.

Overhead and Sensitivity Analysis.
In this subsection, the performance of the gBalloon and the gVirt in a single VM environment is compared. High global graphics memory sizes of 384 MB and 1024 MB are set for the VMs of the gBalloon and the gVirt, respectively. Figure 9 shows the   adaptive behavior in the GPU memory slots of the VMs over time when valley is performed with the dynamic GPU memory expansion policy of the gBalloon. Valley is composed of 18 scenes in total, and the amount of GPU memory required is di erent for each scene. When valley is executed rst, the required amount of GPU memory is increased sharply, and the gBalloon expands three slots in 2 second intervals. en, one slot is expanded for several scenes. e number of slots is increased up to 13, and the size of the high global graphics memory of the VMs is increased to 832 MB. Figure 10 shows the performance of gBalloon for each scene and the overall performance, which is normalized to that of the gVirt. As shown in Figure 10, the overall performance of the gBalloon is lower by approximately 1.9% than that of the gVirt. is is because the slots are increased one by one, resulting in performance degradation due to the temporary lack of GPU memory despite the sharp increase in the amount of GPU memory required in the rst scene. However, this performance degradation is negligible. From the 10th scene when the number of slots becomes 12, the performance degradation disappears due to the frequent expansion requests and the lack of GPU memory. us, the FPS values of the gVirt and the gBalloon are similar.

Related Works
Kato et al. [35], Wang et al. [36], Ji et al. [37], and Becchi et al. [38] proposed technologies for solving the problem of insu cient GPU memory when compute uni ed device architecture (CUDA) is performed in the NVIDIA GPU environment. When the amount of GPU memory is insu cient, the data in the GPU memory are moved to the system memory to secure space in the GPU memory, which is allocated to the applications. However, this copy operation has large overhead when performed at runtime, and the user must use a modi ed API.
Kehne et al. [39] and Kehne et al. [40] proposed a swap policy for reducing the overhead at runtime and improving the resource fairness among GPU applications and the utilization of GPU memory. GPUswap divides the bu er into chunks of a xed size, randomly selects the chunk of an application that occupies the largest amount of GPU memory, and moves the chunk to the system memory when the GPU memory is insu cient. GPUswap randomly selects chunks from applications that occupy the largest amount of memory. However, because the chunk to be removed from the system memory is randomly selected, the performance of the corresponding applications may be degraded if highly reusable data are removed from the GPU memory. To reduce this overhead, GPrioSwap determines the priorities of the chunks by pro ling the GPU memory access counts of the GPU applications and moves the chunk with the lowest priority when the GPU memory is insu cient.
Studies have also been conducted to prevent program crashes when the GPU is shared between containers. Kang et al. [41] proposed a solution that proposes the amount of GPU memory that can be allocated to each container. When a container asks to use more than the limited GPU memory size, ConVGPU rejects the request. In contrast, when the GPU memory is insu cient, ConVGPU lets the container wait until GPU memory becomes available even if the requested amount of memory is less than the limited memory size. However, these studies were targeted at discrete GPUs whose data are transferred through PCIe bus and cannot be directly applied to the heterogeneous system architecture. In this architecture, the system memory is used as the GPU memory, and the data copying between the CPU and the GPU is carried out through a zero-copy bu er.   To improve the memory efficiency in the hypervisor environment, the memory overcommitment technique that decreases or increases the memory allocated to VMs is used. Waldspurger [23], Zhou et al. [24], Zhao et al. [25], Guo [26], Kim et al. [27], and Lu and Shen [28] periodically profiled the access frequencies of pages by nullifying the translation look-aside buffer (TLB) entries of randomly selected pages. Based on this, the least accessed pages are returned when the amount of memory is insufficient. However, this method has a problem because performance degradation may occur due to the nullification of the TLB entries. Furthermore, in [26], [27], [28], and [29], the problem of an inability to respond to sudden changes in VMs' memory demands due to the cyclic overcommitment exists. To solve this problem, the memory pressure aware (MPA) ballooning [27] applies different memory return policies by distinguishing the degree of memory pressure between an anonymous page and a file page. e MPA reduces the performance degradation caused by page return by setting the page with a high probability of becoming the least accessed as the object of return using Linux active and inactive lists. Furthermore, the MPA responds to the VMs' unexpected memory requests by immediately reallocating the memory to sudden memory requests and returning the memory slowly.
Recently, Park et al. [22] proposed a dynamic memory management technique for Intel's integrated GPU called DymGPU that provides two memory allocation policies: size-and utilization-based algorithms. Although DymGPU improves the performance of VMs by minimizing the overlap of the graphics memory space among VMs and thus reduces the context switch overhead, DymGPU's allocation is still static, and the memory size cannot be changed at runtime.

Conclusion and Future Works
In GPU virtualization, due to the static allocation of GPU memory, the performance of VMs that require more GPU memory can be degraded or the GPU application can crash. e gBalloon, proposed in this paper, improves the performance of VMs due to the lack of GPU memory by dynamically adjusting the GPU memory size allocated to each VM. Moreover, the gBalloon detects the increase in overhead due to GPU memory sharing and reduces the GPU memory size of the VMs that unnecessarily occupy a large amount of GPU memory. Consequently, the GPU context switch time is decreased, and the performance of the GPU applications is increased. Furthermore, the performance of the CPU applications is also guaranteed because the CPU load is reduced. e study demonstrated through experiments that the performance of the gBalloon improved by up to 32% when compared with the performance of gVirt with 1024 MB of high global graphics memory.
Currently, the gBalloon increases or decreases only the spaces at both sides to adjust the GPU memory space allocated to VMs. is problem can be solved by allocating non-consecutive spaces of small slot units rather than consecutive GPU memory spaces to VMs. We are currently investigating this issue.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.