Performance Modeling of Database Servers in a Telecommunication Service Management System

Transcription

1 ICDT : The Seventh Internationa Conference on Digita Teecounications Perforance Modeing of Database Servers in a Teecounication Service Manageent Syste Maria Kih, Paya Aani, Anders Robertsson, Gabriea Radu, Manfred Derantz, and Berti Aspernäs 3 Dept. of Eectrica and Inforation Technoogy, Lund University, Sweden Dept. of Autoatic Contro, Lund University, Sweden 3 Ericsson AB, Karsrona, Sweden {aria.ih, paya.aani, anfred.derantz}@eit.th.se uinita.radu@gai.co, andersro@contro.th.se, berti.aspernas@ericsson.co Abstract Resource optiization echaniss, as adission contro and traffic anageent, require accurate perforance odes that capture the dynaics of the syste during high oads. The ain objective of this paper is to deveop an accurate perforance ode for database servers in a teecounication service anageent syste. We investigate the use of a server ode with oad dependency. Concurrent requests add oad to the syste and decrease the server capacity. We derive expicit equations for the state probabiities, the average nuber of jobs in the syste and the average response ties. Further, we present soe heuristics on how to tune the paraeters for given easureent data. Aso, using testbed experients, we vaidate that the ode accuratey captures the dynaics of a database server with write-heavy woroad. Index Ters Perforance anageent; teecounication systes; queuing theory; database servers. I. ITRODUCTIO Resource anageent of server systes has gained uch attention in the ast years, since poory anaged resources can severey degrade the perforance of a coputer syste. The experience is that enterprise servers are often the bottenecs, whereas the networ bacbone is often underutiized. Therefore, the server systes ust provide perforance guarantees which satisfy the service-eve agreeents (on deay, QoS, etc). Aso, the syste ust provide gracefu perforance degradation during overoad. However, a optiization techniques require accurate perforance odes of the invoved coputing systes. The operation region is ainy high traffic oad scenarios, which eans that the coputing systes show non-inear dynaics that needs to be characterized accuratey. A software syste is basicay a networ of queues, as exapes, the CPU ready queue, seaphore queues, socet queues, and I/O device queues, which store requests in waiting of service in the processors. Therefore, queuing odes can be used when describing the dynaic behavior of server systes [] [] [3] [4]. In a previous wor [], we have shown that web servers with dynaic content can be odeed as singe server queuing systes with processor sharing, where the high oad dynaics can be captured with an M/M/ syste. However, this resut is ony vaid for systes with CPU intensive woroad. Soe recent experients on databases have shown that the high oad dynaics of database servers are copetey different for queries invoving write operations [5]. Since database servers are iportant coponents in Teecounication service anageent systes, it is, therefore, iportant to deveop new odes for database servers with write-heavy operations. The concept of oad dependent server (LDS) odes in which the response tie of the jobs in the syste is a function of the service tie of the jobs and current nuber of jobs waiting to be serviced has, to the best of our nowedge, firsty been introduced in [6]. Ra et a. [7], Curie et a. [8] and Perros et a. [6] used standard benchars for woroad generation and aso regression odes to capture the syste dynaics. A uti-step ode paraeter caibration strategy was used for fine tuning of the paraeters in the ode. The resuting odes were cassified as data driven odes. Mathur and Apte [9] presented a queuing networ ode which represents the oad dependent behavior of the LDS. Their ode was not anayzed theoreticay and was ony vaidated with siuations. A theoretica anaysis of the D/G/ and M/G/ odes with oad dependency assuptions was presented in [] by Leung. These odes were deveoped to be used in congestion contro in broadband networs. In this paper, we add the oad dependency behavior to an M/M/ ode. The steady state probabiities, average nuber of jobs in the syste and average response ties are deterined using queuing theory. Aso, we perfor the sae anaysis for the case where the queue is iited. The ode has a sipe structure and can be tuned for various oad and database configurations. Further, in order to tune the paraeters of the ode to represent the current database and oad setup, effects of variations of each paraeter on the ean response tie of the queries sent to the database as a function of ean effective Copyright (c) IARIA,. ISB:

2 ICDT : The Seventh Internationa Conference on Digita Teecounications arriva rate has been studied. Furtherore, soe heuristics for tuning the ode paraeters are introduced. By eans of these heuristics, the ode paraeters can be tuned to atch the easureents fro the database in a few steps. Finay, eans that previous wor on perforance odeing of server systes is not appicabe since they assue CPU-intensive woroad. Request Request Figure. M/M/ ode. Repy Manageent Syste (MAS) Repy Other traffic Database nodes (Ds) Figure. Teecounication service anageent systes. experienta resuts show that this ode is abe to capture the high oad dynaics of the database server. This paper is organized as foows. The description of the syste is introduced in Section II. Section III is dedicated to introduction of the oad-dependent server ode. Experient setups and resuts are shown in Section IV. Section V concudes the paper. II. SYSTEM AD PROBLEM DESCRIPTIO In teecounication service oriented architectures, as obie networs, a services, either user services as teephony, or adinistrative services as ocation updates or biing, are handed by a service anageent syste with its own networs and protocos, as iustrated in Figure. The service anageent systes have a copex architecture, usuay ipeented as arge distributed server systes, with Manageent appication servers (MAS) processing service requests fro the teeco networs, and databases (Ds) storing subscriber and service data. The Ds are oaded with service traffic fro other networs. A signaing is perfored across IP networs, with standardized appication ayer protocos, as Lightweight Directory Access Protoco (LDAP) or Sipe Object Access Protoco (SOAP). The syste is required to have high reiabiity for varying traffic oads, where the Ds ay be overoaded by the traffic coing fro other networs. The nodes can be owned by different networ operators, iiting the avaiabe inforation of traffic oads and service progress. A signaing is perfored across IP networs. In this paper, we focus on the odeing aspects of database servers in teecounication service anageent systes. The objective is to deveop a perforance ode for the database server that captures the dynaics during high oads. The perforance ode can be used in resource optiization schees, as adission contro systes, in order to axiize the throughput of the database server, whie eeping soe atency constraints. One of the chaenges for these database servers is that they have a write-heavy woroad, which eans that the CPU is not the bottenec during high oads. This III. LOAD-DEPEDET SERVER MODEL Perforance odes are aied to be used in the process of designing anageent entities for server systes. Therefore, the perforance ode shoud capture the doinant dynaics of the server syste. Most service perforance etrics such as response tie, service rate and processing deay depend on queue state dynaics. A. Singe server queues For the objective of perforance contro, sipe odes, based on the assuption of a singe server queue, are often preferred. The ode shoud ony capture the doinating oad dynaics of the syste, since a we-designed contro syste can hande any ode uncertainties []. The cassica M/M/ ode, where a singe-server queue processes requests that arrive according to a Poisson process with exponentia distributed service ties, see Figure, has been shown to accuratey capture the response tie dynaics of a web server syste []. B. M/M/ ode with oad dependency (M/M/-LDS) In this paper, we propose to add oad dependency to an M/M/ syste. In a oad-dependent server odes, the service tie for a request wi be dependent on the nuber of concurrent requests in the syste. This oad dependency wi ode effects of the operating syste, eory use, etc., which ay cause service degradation when there are any concurrent jobs in a coputing syste [8]. In the experient section, we wi show that the M/M/-LDS ode accuratey captures the behavior of write-heavy woroad. The properties of the oad dependent M/M/ ode (M/M/-LDS) are set by an exponentia distributed base processing tie x base = / and a dependency factor (f). When a request enters the syste, it gets the base processing tie x base assigned to it. A singe request in the syste wi aways have a processing tie of x base. Each additiona request inside the syste increases the residua wor for a requests inside the syste (incuding itsef) by a percentage equa to the dependency factor f. When a request eaves the syste a other requests have their residua wor decreased by f percent again. This eans that if n concurrent requests enter the syste at the sae point, they wi a have a processing tie of x ( n) x ( f ) n s base () A specia case is when f =. It eans that there is no oad dependency, and a requests wi have processing tie x base. The syste can process a axiu of concurrent requests at each tie instance. Any additiona request wi Copyright (c) IARIA,. ISB:

3 ICDT : The Seventh Internationa Conference on Digita Teecounications have to wait in the queue. ew requests arrive according to a Poisson process with average rate. Figure 3. Iustration of M/M/-LDS ode as a Marov chain. Therefore, the syste can be odeed as a Marov chain as iustrated in Figure 3. The average service rate of the syste that depends on the nuber of concurrent requests in the syste, is derived as foowed: ( f ) if if ( f ) By soving the baance equations, stationary probabiity distribution of existence of concurrent requests in the syste is cacuated as beow: ( ) ( f ) if! ( )( ) ( f ) if! As the su of the probabiities of a possibe states equas to one, can be derived as foows: ( ) ( ) ( f ) ( f )! ( )!( ( f ) ) The stabiity condition in this case is ( f ) (6) The average nuber of requests in the syste,, can be cacuated as beow: ( f ) ( f ) ( ) ( )! 3 ( f ) ( f ) ( ) ( f ) ( ( )( f ) ) ( )!( ( f ) ) ( ) ( f ) + ( f ) ( f ) ( f ) (3) (4) (5) (7) Finay by eans of Litte s theore, the average tie each request spends in the syste, T, can be derived as foows. T C. M/M//n ode with oad dependency (M/M//n-LDS) In case that the queue is iited to n positions, the probabiity for an epty syste,, can be deterined as foows. This queuing syste is naed as M/M//n-LDS. I II III I ( f )! ( ) nn n ( f ) II f III n n!( ( ) ) ( ) ( f ) ( )!( ( f ) ) Further, the average nuber of requests in the syste is as foows: ( f)! ( ) f f n n n 3 D D D 3 n n 3 ` nn n f n n ` nn f n ( f ) n ( ) f f! f D! D f n nn n f f f n 3 D 3 f f! f (8) (9) () Finay, the average response tie for a request can be derived using Litte s theore. D. Paraeter tuning In a teeco syste with atency constraints, the doinant dynaic of the syste is often characterized by the average response tie, T, when varying the average arriva rate,. Tuning of the paraeters of the oad dependent server ode Copyright (c) IARIA,. ISB:

4 ICDT : The Seventh Internationa Conference on Digita Teecounications in a way that it fits the easured data fro the actua server syste is a necessary step in odeing of such systes. Assuing that and T are easureabe, and therefore, nown, there are three ain paraeters for the M/M/-LDS ode,, f and to tune in order to fit the ode on the easured data. Further, for the M/M//n-LDS there is an extra paraeter, n, to tune. Therefore, in Figures 4-8, we have iustrated the effect of changing ode paraeters. In the rest of the paper, this graph wi be caed the /T graph. In each figure, we have assued that two (three) of the paraeters are fixed and the one that is entioned is the variabe. As the equations for cacuating the ean response tie, is rather copex and the paraeters are interdependent, ore than one set of paraeters can be fit on the easured data. Thus using these figures, we can achieve a heuristic rue for tuning the paraeters of the oad dependent server ode. In the cases where the M/M/-LDS ode is used, the first paraeter to be tuned is the nuber of servers,. As it can be seen in Figure 4, by increasing the axiu nuber of concurrent requests that can be processed in the syste, the inear part of the /T graph wi be shorter and the exponentia rising rate of the graph is increased. In this case it is assued that (f, ) = (.7, ). The second paraeter to be tuned is the dependency factor, f. As shown in Figure 5, by decreasing the dependency factor, the inear part of the /T graph is increased, however, the change is sower than in the case where is decreased. On the other hand the exponentia rising rate of the graph is increased in coparison with the case where is decreased. Here, it is assued that (, ) = (3, ). The effects of changing on the/t graph whie fixing the two other paraeters is iustrated in Figure 6. As shown in the figure, by increasing in equa steps, the /T graph wi be shifted to the right in equa steps. In this case, the rate of rising of the graph is decreased. In this case, (, f) = (3,.7). Figure 5. Variations of /T graph for a specia scenario with f as variabe when (,) = (3, ). Figure 6. Variations of /T graph for a specia scenario with as variabe when (, f) = (3,.7). In cases where the M/M//n-LDS ode is used, there wi be a saturation of the response ties when the oad is high enough to overoad the queue. Here it is assued that the defaut vaues are (, n, f, ) = (4, 5,.6, ). Figure 7 and Figure 8 show the effects when varying and f respectivey. In each case the vaues of the other three paraeters are constant. The genera effect of changing the paraeters is siiar as for the case with the infinite queue, with the difference that the response ties saturate when the oad is high. Figure 4. Variations of the /T graph for a specia scenario with as variabe when (f,) = (.7, ). Figure 7. Variations of /T graph for a specia scenario with as variabe when (n, f, ) = (5,.6, ). Copyright (c) IARIA,. ISB:

5 ICDT : The Seventh Internationa Conference on Digita Teecounications Figure 8. Variations of /T graph for a specia scenario with f as variabe when (, n, ) = (4, 5, ). IV. EXPERIMETS AD RESULTS To vaidate the proposed ode, we have perfored a series of experients in our server ab. We deveoped a database server testbed with a traffic generator and a MySQL 5..4 database server, see Figure 9. The coputers were connected to a oca Fast Ethernet Mbit/s networ. A. Testbed The traffic generator was ipeented in Java, using the JDBC MySQL connector, and it was executed on a coputer with an AMD Pheno II X6 55T Processor at.8 GHz and 4 GB ain eory. The operating syste is Ubuntu.4. LTS. The traffic generator used woring threads and generates MySQL queries according to a Poisson process with average rate queries per second. The behavior of the traffic generator was vaidated in order to guarantee that it was not a bottenec in the experients. The database server has severa reations with the sae structure but with different nuber of tupes. The axiu nuber of aowed concurrent connections is set to. The structure of the reations coes fro the Scaabe Wisconsin Benchar [] with iion tupes. Two basic types of queries are used, SELECT (read) and UPDATE (write). The queries oo ie this SELECT * FROM <reation> WHERE unique=?; UPDATE <reation> SET unique=? WHERE unique=?; The question ars are repaced with unifory distributed rando nubers fro zero to ten iion. Traffic Generator Figure 9. Database server testbed. MySQL Figure. Perforance of the M/M//n-LDS queuing ode in odeing steady state dynaics of a MySQL database server using ony update queries. B. Resuts The dynaics of a database server highy depends on the ix of requests, since Seect and Update queries require different aount of server capacity. Therefore, we have perfored experients with varying woroad ix. Figures and show the resuts fro experients where the arriva rate is varied fro ow oad to high oad. The graphs show the average response ties of update queries as a function of the arriva rate. We have fitted M/M//n-LDS odes for the data using the tuning steps in Section III. In both scenarios, the CPU utiization was very ow, aso for high oads. The axiu CPU oad was about 5%. In Figure, the woroad is based on % Update queries. The fitted ode in this case has the foowing paraeters (, n, f, ) = (3, 8,.75, 37.). In order to ode the networ deays, we have added a bias of.3 seconds in the average response ties of the proposed ode. Figure depicts the sae experient setup when using a ix of 5% Seect and 75% Update queries. The fitted M/M//n-LDS ode in this case has the foowing paraeters (, n, f, ) = (6, 73,.44, 35.). In order to ode the networ deays, we have added a bias of.3 seconds in the average response ties of the proposed ode. Figures and verify that the proposed ode can represent the average dynaics of a database server with write-heavy woroad very we. V. COCLUSIOS AD FUTURE WORKS Resource anageent schees require accurate perforance odes that capture the doinant dynaics of the syste in high oads. For server systes with write-heavy woroad, oad dependent server (LDS) odes can be used to ode the dynaic overhead effects of concurrent requests. In this paper, queuing theoretic etrics ie average nuber of the requests in the syste, average tie in the syste for each request and the steady state probabiities for M/M/-LDS odes with both uniited and iited queues have been derived. Further, it has been shown via experients that the M/M//n-LDS ode represents the average dynaics of the database server very we. The resuts are aied at singe Copyright (c) IARIA,. ISB:

6 ICDT : The Seventh Internationa Conference on Digita Teecounications database servers, and not aied at data centers, which have different dynaics. Furtherore, we wi use this ode in order to design controers and state estiators for resource anageent and adission contro of database servers. VI. ACKOWLEDGMETS The authors at Lund University are ebers of the Lund Center for Contro of Copex Engineering Systes. The wor is party funded by the Swedish Research Counci, grant VR REFERECES [] J. Cao, M. Andersson, C. yberg and M. Kih, Web Server Perforance Modeing using an M/G//K*PS Queue, Proc. of the Internationa Conference on Teecounication, 3. [] J. Diey, R. Friedrich, T. Jin, and J. Roia, Web server perforance easureent and odeing techniques, Perforance Evauation, Vo. 33, o., 998. [3] D. A. Menascé and V. A. F. Aeida. Capacity Panning for Web Services, Prentice Ha,. [4] R. D. van der Mei, R. Hariharan, and P. K. Reeser, Web server perforance odeing, Teecounication Systes, Vo. 6, o. 3,. [5] M. Kih, G. Cedersjö, A. Robertsson, B. Aspernäs, Perforance easureents and odeing of database servers, Sixth Internationa Worshop on Feedbac Contro Ipeentation and Design in Coputing Systes and etwors,. [6] H. Perros, Y. Daery, and G. Pujoe, Anaysis of a queuing networ ode with cass dependent window fow contro, IFOCOM 9. Eeventh Annua Joint Conference of the IEEE Coputer and Counications Societies, IEEE, pp vo., May 99. [7] A. Ra, A. Sguegia, "Instantaneous Load Dependent Servers (ilds) Mode for Web Services," In Proceedings of the Internationa Conference on Copex, Inteigent and Software Intensive Systes,. [8] Curie, M. and Puigjaner, R., Using oad dependent servers to reduce the copexity of arge cient-server siuation odes, Perforance Engineering, Springer-Verag Berin Heideberg, pp. 3-47,. [9] V. Mathur and V. Apte, A coputationa copexity aware ode for perforance anaysis of software servers, in Proc. of Modeing, Anaysis and Siuation of Coputer and Teecounication Systes (MASCOTS), IEEE Coputer Society, pp , 4. [] Kin K. Leung, Load-dependent service queues with appication to congestion contro in broadband networs, Perforance Evauation, Vo. 5, Issue, pp. 7-4, October. [] K J. Åströ and B. Wittenar, Coputer Controed Systes, Upper Sadde River, J: Prentice Ha, 997. [] D.J. DeWitt, The Wisconsin benchar: Past, present, and future, The Benchar Handboo for Database and Transaction Processing Systes,, 99. Figure. Perforance of the M/M//n-LDS queuing ode in odeing steady state dynaics of a MySQL database server using ixed queries. Copyright (c) IARIA,. ISB: