# Realistic Tenant Traces for Enterprise DBaaS

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4 (b) Tenant with low activity 1 1 (a) Regular tenant (c) Demo system used actively until end of trial (d) Demo system used only at beginning and end of trial Fig. 3: Different usage patterns for regular tenants and trial customers day. The pronounced lunch-break drop for tenant request rates around noon motivates the use of a double Gaussian function as follows: (t µ1 )2 (t µ2 )2 Rd (t) = a exp( ) + b exp( ) + c. (1) 2 2σ1 2σ22 We parametrize (1) such that m(rd (t) Qd (t)) is minimal. We denote the mean squared error by m( ). We opted for the simple model (1) because it fits the typical working day rhythm with a single lunch break. Future work could include other functions or more involved versions of (1), e.g. triple, asymmetric Gaussian functions [2]. We randomly chose a work day and fit (1) to it. Figure 4 shows the original trace (blue) and the least-squared fitted curve (green) with mean average absolute error (MAPE) of 43% and coefficients a = 55.6, µ1 = 59., σ1 = 8.9, b = 75.24, µ2 = 88.84, σ2 = 1.64, c =.9. For modeling a working week w, we suggest shifting Rd (t), i.e. X Rd (t mod 144), Rw (t) = t [1,144 5] adjusting c appropriately. For weekends and public holidays indicator variables are needed to model the decrease in requests. In order to see how well (1) predicts tenant traces, we randomly chose 2 work days and calculated the MAPE between the aggregated tenant trace predicted by (1) and the actual aggregated load. The arithmetic average over the 2 MAPEs is 39% which clearly indicates how well (1) generalizes to other work days. So far, we have modeled the aggregated tenant request rates. We obtain the request rate of a single tenant u by scaling Rw (t), i.e. rw,u (t) = srw (t) by an appropriately chosen s. The distribution of tenant sizes provides a guideline on how to obtain such scale factors s by assuming requests to be proportional to database size. By adding random noise e(t) to the working day pattern, we can create diversity among equally scaled tenant traces. We suggest using a normally distributed error, i.e. x2 1 (2) e(t) = exp( 2 ). 2σt σt 2π such that σt = 3 for all t except t {µi 5, µi + 5} with i {1, 2} where σt = 1 better captures the higher volatility in load. The orange line in Figure 4 shows an example of a tenant created by (1) and (2). For demo tenants, we also rely on Rd (t). Here, a much smaller scale factor is appropriate and a variable that indicates the limited time window of activity. Similar to regular tenants, adding random noise leads to the desired variety in tenants. For modeling sizes of tenants, we already remarked that they follow a zipfian distribution. We chose to fit s(u) = a + bu c. (3) We assume that tenants are ordered by size non-increasingly. The position u [1,..., 1] in the sequence of sizes corresponds to the tenant. When we fitted (3), we obtained a MAPE of 7% for the following parameters a =.15, b = 15.65, c =.83. (4) The red line in Figure 1 shows (3) with parameters (4). Having discussed how to generate tenant traces synthetically based on our observations, we consider the case that one has access to a limited number of tenant traces and needs to generate more tenant traces.

5 1 Fit plus Normal Noise Fit Real Data Request rate in (%) : : 1: 9: 8: 7: 6: 5: 4: 3: 2: 1: : Time (in hours) 24: 23: 22: 21: 2: 19: 18: 17: 16: 15: 14: : Fig. 4: Aggregated vs Generated Request Rates IV. BOOTSTRAPPING As mentioned in Section I, it is difficult to obtain real-world tenant traces. While the previous chapter dealt with modeling tenant traces, we consider enlarging a set of given tenant traces in the following. We provide a straight-forward bootstrapping methodology with a single parameter, the bootstrap window size. For our use case, we show how to identify an appropriate value for this parameter. In the server logs we obtained, a tenant trace comprises the request rates of a tenant across a 4-month-period aggregated in ten-minute intervals. We refer to a point in discretized time, such as the ten-minute interval in our case, as a tick in the tenant trace. We were only granted access to a subset of the traces, 1 tenants in total. However, this random sample gives a realistic impression of the overall customer base. Unfortunately, the sample is not large enough to conduct meaningful experiments with realistically-sized server farms. For example, in October 27, the SaaS CRM vendor RightNow had 3 tenants distributed across 4 MySQL database instances [21]. To simulate a realistically sized DBaaS scenario, it is therefore necessary to increase the pool of tenant traces. Here, we suggest bootstrapping in order to enlarge the set of tenant traces such that the trace of a bootstrapped tenant shows the temporal characteristics of a working week, during a loaded workday, an active server holds 1 1 tenants, each tenant has a realistic size and trace volume, and, bootstrapped tenants resemble the sample tenants while being sufficiently distinct from them and each other. In our methodology we follow [22]. Our methodology can naturally be combined with the generation of tenant traces as shown in the previous section. This may be interesting for example in the case where certain work day patterns are not present in the traces. A. Bootstrapping Process Our bootstrapping process produces for each original tenant trace, which we call a parent trace, a fixed number c of child traces. Figure 5 shows a schematic overview of the bootstrapping process. Apart from deciding on the trace pattern, we also need to assign a size to the child tenant. Based on our observations in Section III, we differentiate between regular tenants and demo tenants. Regular tenants all have comparably similar request rate patterns but highly varying sizes. Demo tenants have irregular usage patterns but exhibit smaller difference in their sizes. Therefore, it seems reasonable to choose size independently of trace pattern for regular tenants. In more detail, our bootstrapping works as follows. From each parent tenant trace, we createcchild tenants. The number of bootstrap copies c is a parameter of the process which we can choose. Each child tenant is then given a size drawn at random from a list of all parent tenant sizes (depending on the parent tenant being a demo or a regular tenant). The process of bootstrapping a parent trace into a single child trace, shown in Figure 5, is as follows: 1) The parent trace is divided into equally sized subintervals of size W with the last subinterval of the trace potentially having size less than W. We call a subinterval a window in the following. 2) The indices of a window of the parent trace correspond directly to the indices of a window in the child trace. Window i spans {iw,iw +1,...,iW +W 1} in both parent and child traces. 3) For each parent window, W values are chosen at random with replacement and uniform probability. These values are placed into the corresponding child window in the order that they are chosen. The quality of the bootstrapping processing depends on the choice of W. Section IV-B provides details. The bootstrapping process results in c times many new tenants, each with a realistic size and a trace that is similar but not identical to its parent. For 1 parent tenant traces, we have 1 c many tenants. By drawing the child tenant size at random from all parent tenant sizes, we doubly ensure that the child is not too similar to its parent as size and request rate influence the load that a tenant puts onto a DBaaS cluster [1]. B. Choosing the bootstrap window size In the following, we describe how to obtain a good value for W which determines the similarity between child and parent

6 first window i-th window N-th window W parent tenant first window i-th window N-th window child tenant W-1 parent tenant c times child tenant Fig. 5: The bootstrapping process for generating realistic tenant load traces. tenant. For a choice of a smallw, we run the risk of all or most c child traces of a single parent tenant trending in unison, as a load spike in the parent may occur in its children around the same ticks. Conversely, a large W causes irregularity and lack of natural smoothness in the children: for example, a window may fall on the boundary between night and workday, and the low-request at a tick during the night and high-request ticks during the workday become intermingled, giving the trace unnatural spikes. The goal is thus to set W such that the deviation between parent and children is high enough, while no unnatural spikes occur. In the following we analyze both phenomena. While the methodology is generally applicable, we use our traces from the previous section as an example. For ease of exposition, we assume c = 5. Deviation between Parent and Child. Figure 6a shows how the similarity between parent and child traces decreases as the size of the bootstrap window increases. Specifically, it shows the mean deviation in load across all ticks between the parent and its bootstrapped children, computed using the Root Means Squared Deviation (RMSD) for each parent/child pair. The figure depicts one of the largest tenants in our trace. Note that the increase of the RMSD flattens out beyond W = 1. Recall that the window size (depicted on the horizontal axis in Figure 6a) corresponds to numbers of ten-minute intervals for which request rates where aggregated in the traces. Controlling Unnatural Spikes. Figure 6b characterizes unnatural spikes in the bootstrapped children. When looking at the amount of change that a parent exhibits in request rates between two adjacent ticks, we define this change to be unnatural when it is larger than the 75-th percentile of all changes in request rates of the parent. Figure 6b, again focusing on a single tenant, shows the percentage of request changes larger than the 75-th percentile for the parent and its children with varying W. For the parent, obviously, this percentage is independent of the window size. For the children, the percentage of unnaturally high changes in requests is the same as for the parent when choosing W = 1. For 2 W 1 it is lower than for the parent. This is because with such small window sizes there is always a relatively high chance for picking a value that has already been picked previously in the same window as the next value. For larger values of W, the children have higher changes in request between adjacent ticks than the parent, i.e. the children become more unnatural. This is because for large window sizes the chance increases that a vastly different value from the value picked for the current ten-minute interval is contained in the window and is picked as the value for the next tick at some point. Based on the deviation and spike criteria, we suggest a bootstrapping window size of 1 as an appropriate value for W for our traces. This choice balances deviation of a parent and its children with unnatural changes between adjacent ticks. V. CONCLUSION AND FUTURE WORK The benchmarking of multi-tenant Database-as-a-Service scenarios is an involved topic on which research only recently started. Often tenant behavior is modeled after private end-user behavior or generated randomly. Here, we have made the point that there are significant differences between private end-user and enterprise on-demand services. As enterprise on-demand providers are more protective with respect to their customer base than public services such as Wikipedia, enterprise tenant behavior is more difficult to obtain. Restrictions and normalizations protect the interest of the involved parties rigorously. In this paper, we have shown ways to overcome restrictions which may occur due to protection of privacy and interests. For usage in benchmarks for testing DBaaS, we note the following on our tenant traces. Our tenant traces are based on requests from real customers from small to mid-sizes enterprises. Although the exact nature of their requests is unknown to us, it is likely to be a so-called mixed workload. Therefore, one could approximate these real-world customer requests via a standard benchmark in a multi-tenancy benchmark which naturally introduces some inaccuracy. However, this is where the modularity of MulTe [1] would provide a benefit: one can simply experiment with different available benchmarks to approximate a range of enterprise on-demand scenarios. Second, companies often do not publicly disclose their exact

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