Even though transaction deadlocks can severely affect the performance of distributed database systems, many current evaluation techniques ignore this aspect. Shyu and Li proposed an evaluation method which takes deadlocks into consideration. However, their technique is limited to exclusive locking. Using this technique, researchers illustrate the impact of deadlocks in the presence of shared locking on distributed database performance

Kuang, Yinghong

Mukkamala, Ravi

English

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N91-23975
A Note on the Performance Analysis of Static
Locking in Distributed Database Systems
Yinghong Kuang and Ravi Mukkamala
Department of Computer Science
Old Dominion University
Norfolk, Virginia 23529.
Abstract
Even though transaction deadlocks can severely affect the perfor-
mance of distributed database systems, many current evaluation tech-
niques ignore this aspect. In [4], Shyu and Li proposed an evaluation
method which takes deadlocks into consideration. However, their tech-
nique is limited to exclusive locking. In this paper, we extend their
technique to allow for both shared and exclusive locking. Using this
technique, we illustrate the impact of deadlocks, in the presence of
shared locking, on distributed database performance.
Index Terms: Distributed databases, exclusive locking, performance mod-
eling, shared locking, static locking, two-phase locking.
https://ntrs.nasa.gov/search.jsp?R=19910014662 2020-03-19T17:46:02+00:00Z
1 Introduction
A distributed database system (DDS) is a collection of cooperating nodes
each containing a set of data objects. A user transaction can enter such a
system at any of these nodes. The receiving node, often referred to as the
coordinating node, undertakes the task of locating the nodes that contain
the data objects required by a transaction.
In order to maintain database consistency and correctness in the pres-
ence of concurrent transactions, several concurrency control protocols have
been proposed [1]. Of these, locking protocols have been widely used in both
commercial and research environments. In static locking, prior to start of
execution, a transaction needs to acquire either a shared-lock (for read op-
erations) or an exclusive lock (for update operations) on each of the relevant
data objects. When transactions with conflicting lock requests are initiated
concurrently, they could be possibly blocked due to a deadlock. Deadlocks
are known to deteriorate performance in both centralized and distributed
database systems [4,6]. In spite of this, several performance studies have
ignored the deadlock problem in their analyses [2,5].
In [4], Shyu and Li proposed an elegant technique to evaluate the re-
sponse time and throughput of transactions in a non-replicated DDS. (In the
rest of the paper, we refer to this as the S-L technique.) Assuming exclusive
locking (i.e., only write operations), they model the queue of lock requests
at an object as a M/M/1 queue [3]. This results in a closed-form for the
waiting time distribution at a node, expressed in terms of the average rates
of arrivals of requests and the average lock-holding time. This technique
consists of two stages. In the first stage, the average transaction response
time and throughput are calculated by ignoring the deadlock. This is an
iterative step that uses the known properties of the M/M/1 queue [3]. In
the second stage, the probabilities of transaction conflicts and deadlocks are
computed. These probabilities are used, in turn, to compute the response
time and throughput in the presence of deadlocks.
In general, a database transaction reads from a set of data objects (the
read-set) and writes on to a set of data objects (the write-set). Assuming
that all accesses are write-only (as in S-L) results in the worst-case per-
formance (with respect to deadlocks and response time) of a DDS. In this
paper, we propose to extend the S-L technique to consider both the the read
and the write operations of database transactions. Using the extended S-L,
we evaluate the effect of deadlocks on distributed database systems.
2
2 Model
Except for the inclusion of read operations, our model is the same as in S-L.
For the sake of completeness, we summarize the DDS model here.
• There are N nodes and D data objects (or data granules in S-L) in
a DDS. The D data objects are uniformly distributed across the N
nodes. A data object may be located at exactly one node.
• Each transaction accesses K data objects. Among these, r. K are
for read-only purpose, and the rest are for read-write. (Obviously,
0 < r < 1.) In other words, a transaction must procure r. K shared
locks and (1 - r) • K exclusive locks.
• Each data object is equally likely to be accessed by a transaction.
• Transaction arrivals into the system is a Poisson process with rate A.
• The communication delay between nodes is exponentially distributed
with mean t.
• The average execution time of a transaction, once the locks are ob-
tained, is _¢.
3 Evaluation Procedure
Since we are only proposing extensions to the S-L model, we do not intend to
repeat the description of their procedure. Instead, we will discuss only the
sahent features of their procedure that are relevant to describe the proposed
extensions.
In Stage 1 of the S-L technique, an iterative procedure is used to eval-
uate the response time and throughput of a DDS ignoring the possibility
of deadlocks. In each iteration, the average waiting time (for exclusive lock
requests) at each of the data objects is computed using estimates of the av-
erage lock-holding times from the previous iteration. By definition, no two
exclusive lock requests can have lock grants on the same object simultane-
ously. Also, assuming that the lock-holding time is exponentially distributed
(with mean 1//z) and that the lock request arrivals form a Poisson process
(with rate Ar = .k • K/D), the distribution of waiting time Wi at an object
i is expressed as (M/M/1 queueing formula [3])
fw,(Y) = (I - p). #o(Y) + Ar(l - p). e -_(I-p)u (I)
where #0(') is the impulse function and p = At//1. Using the waiting time
distribution, the waiting times at the K data objects are randomly gener-
ated. These are used, in turn, to derive new estimates for the lock-holding
times (1/#). The iterations stop when two successive computations of aver-
age waiting time estimates are very close.
When we consider both shared and exclusive locks, the problem of es-
timating the waiting time distributions becomes difficult. Since two shared
lock grants on the same object may exist simultaneously, and an exclusive
lock may not be granted while another shared or exclusive lock is already
granted, the queueing discipline at a node is complex. Such complex queue-
ing disciplines are analytically intractable [3]. For this reason, we propose to
use simulation to solve the queueing model. Given the total rate of arrival
of lock requests At, the shared lock ratio (r), and the average lock-holding
time (1/#), the queue at an object may be simulated. From here, the waiting
time distribution may be obtained in the form of a table. Once the waiting
time distribution is obtained, the same iterative procedure as in Stage 1
of S-L may be adopted to compute the response time when deadlocks are
ignored. As in S-L, transaction response time is defined as the time between
the instance the lock requests are sent and the time the last grant request
is received by the coordinating node.
In Stage 2, the probabilities of transaction deadlock and restart are com-
puted. These are then used to compute response time and throughput in
the presence of deadlocks. When we assume that transactions only make
exclusive lock requests, the expression for the probability of conflict between
any two transactions is given by,
Pc = 1 (DKK) (2)
However, when we consider both shared locks and exclusive locks, the prob-
ability of conflict is reduced. In this case the probability of conflict is given
by,
K-K' ]p, : , _ _ ', (3)
where K' = r.K and represents the average number of shared locks; (K-K')
is the average number of exclusive locks per transaction. Clearly, when
r = 0, Pc = P'; when r = 1, Pc' = 0; and in all cases, Pc _> P'.
By replacing Pc with Pc', the procedure suggested in S-L may be applied
to obtain the desired performance metrics.
4 Results
Using the extended S-L technique, we obtained a number of interesting
results that illustrate the effect of deadlocks on database performance. These
are summarized in Figures 1-5. We have verified our results with those
obtained in [4] for the all exclusive locks case (r = 0). We make the following
observations.
As expected, the presence of shared locks has a substantial impact on
the probability of deadlock occurrence (Fig. 1). When only 1/3 of
the accessed data objects are updated (i.e., r = 2/3), the probability
of deadlock is considerably small as compared to when all objects are
updated (r = 0).
The observations about the deadlock probabilities are also valid for
restart probabilities (Fig. 2).
Transaction response times are also quite sensitive to the ratio of
shared locks (Fig. 3). Here, we compare the response times when
deadlocks are ignored (computed in Stage 1) with those obtained when
deadlocks are considered (computed in Stage 2). The effect of dead-
locks is more predominant at higher transaction loads and with smaller
values of r. When r = 2/3, the effect of deadlocks is not significant on
response time.
The effect of deadlocks on response time is decreased with the increase
in the number of data items (Fig. 4). Obviously, this is due to the
decrease in probability of conflicts and hence a decrease in deadlock
occurrence. For r = 2/3, this effect is almost insignificant. For r = 1/3
and r = 0, deadlocks seems to have a noticeable effect on response
time.
Fig. 5 summarizes the effect of the number of locks per transaction on
response time. When K is small, the probability of deadlock is negli-
gible, and hence its effect on response time is small. At higher values
of K, the effect of deadlocks on response times is significant. Similarly,
at smaller values of r, the effect of dedalocks is more apparent.
5 Conclusion
In [4], Shyu and Li presented an elegant technique to evaluate the perfor-
mance of distributed database systems in the presence of deadlocks. Their
technique assumed only exclusive locks and thus representing the worst-case
effects of deadlocks. In this paper, we have extended their technique to al-
low both shared and exclusive locking. Using the extended technique, we
evaluated the the effect of number of data objects, the number of data ob-
jects accessed, and the ratio of read operations on transaction response time.
These results also indicate the importance of considering both shared and
exclusive lock requests for response time evaluations.
References
[1] P.A. Bernstein, V. Hadzilacos, and N. Goodman, Concurrency Control
and Recovery in Database Systems, Addison-Wesley, 1987.
[2] A. Hac, "A decomposition solution to a queueing network model of a
distributed file system with dynamic locking," IEEE Trans. Software
Eng., vol. SE-12, no. 4, pp. 521-530, Apr. 1986.
[3] L. Kleinrock, Queueing Systems, Vol. I, New York: Wiley-Interscience,
1975.
[4] S.-C. Shyu and V. O. K. Li, "Performance analysis of static locking in
distributed database systems," IEEE Trans. Computers, vol. 39, no. 6,
pp. 741-751, June 1990.
[5] M. Singhal and A. K. Agrawala, "Performance analysis of an algorithm
for concurrency control in replicated database systems," Proc. ACM
SIGMETRICS Conf. Measurement Modeling Comput. Syst., 1986, pp.
159-169.
[6] Y. C. Tay, R. Suri, and N. Goodman, "A mean value performance
model for locking in databases: The no-waiting case," Y. ACM, vol. 32,
no. 3, pp. 618-651, July 1985.
Probability
0.005
0,004
0.003
0.002
0001
K = 3 • r = 2/3
D = 200 +r = 1/3
Or=0
lr =20
i]=0.2
 =o.ol
A
2 4 6 8
Arrival rate(trans/sec)2
Fig.l. Deadlock probability with different
read ratios
0.0025
0.0020
0,0015
Probability
0.0010
0.0005
K = 3 Ar = 2/3
D=200 ÷r=1/3
Or=0
r = 20
=2
_=0.2
g=o.ol
2 4 6 8
Arrival rate(trans/sec)2
Fig.2. Restart probability with different
read ratios
Response
time
(sex)
1.15
1.1o K = 3 De: Deadlock considered.
d = 200 DI: Deadlock ignored.
1.05 lr =20
1 m =2
I i'i= 0.2 /O DC
o,5[ s=o.o] /
o9ol ,r=l j ,+
" t At= 2/3
Or= 0 DI
0.75 ]_
0.70 DIDcI
06_
0 2 4 6 8
Arrival rate(trans/sec) _.
Fig.3 Comparison of response time when
deadlock is considered and deadlock is ignored.
Response
time
(sex)
0.85
K = 3 De: Deadlock considered;
D = 400 DI: Deadlock ignored.
z" =20
0.80
m =2
ti = 0.2
I _=o.01 /,,_0.75] Xr=l __
t •r = 2/3 DI
+r 1/3
0.7o IX
0.65_
o6
Fig. 4
2 4 6 8 10
Arrival rate(_ans/sec) ;t
Response time with high number of data objects.
Response
time
(sec)
1.6
1.4
1.2
0.8
0.6
0.4
2 =4 jDC
D=400
r = 20
¢.o =2
i'i = 0.2 ///+ DC_=o.o_
"r=2/3 / _ DI
+r= 1/3 J /7{" DI
.,:o p/ D(
_..¢f
 oI
e-'-----'i "_ DC: Deadlock considered.
DI: Deadlock ignored.
0 1 2 3 4 5
K
Fig.5. Comparison of response time with
different number of lock requests.


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