Data replication and transaction deadlocks can severely affect the performance of distributed database systems. Many current evaluation techniques ignore these aspects, because it is difficult to evaluate through analysis and time consuming to evaluate through simulation. A technique is used that combines simulation and analysis to closely illustrate the impact of deadlock and evaluate performance of replicated distributed database with both shared and exclusive locks

Kuang, Yinghong

Mukkamala, Ravi

English

NASA Technical Reports Server

\ N91-25955
Performance Analysis of Static Locking in Replicated Distributed Database Systems
Yinghong Kuang
Ravi Mukkamala
Department of Computer Science
Old Dominion University
Norfolk, Virginia 23529.
Abstract
Data replications and transaction deadlocks can severely af-
fect the performance of distributed database systems. Many
current evaluation techniques ignore these aspects, because it
is difficult to evaluate through analysis and time-consuming to
evaluate through simulation. In this paper, we use a technique
that combines simulation and analysis to closely illustrate the
impact of deadlock and evaluate performance of replicated dis-
tributed database with both shared and exclusive locks.
1. Introduction.
A distributed database system fDDS) is a collection of co-
operating nodes each containing a set of data items. A user
transaction can enter such a systelu at ally _)f tl,.se ,iod('s. 'l'lw
receiviag i,ode, often referred to as the r'oo;'dm.t._ 9 node, uq-
dertakes the task of locating the nodes that contai,_ the data
items required by a transaction.
In order to maintain database consistency and correctness
in the presence of concurrent transactions, several concurrency
control protocols have been proposed [11. Of these, the most
commonly used are time-stamping and locking protocols. Lock-
ing protocols have been widely used in both commercial and
research environments, in static locking, prior to start of exe-
cution, a transaction needs to acquire either a shared-lock (for
read operations) or an exclusive lock (for update operatio,ls) on
each of the relevant data items.
Data replication is used to improve the performance of local
transactions and the availability of databases. In replicated
databases, one data item may have more thai, one copy in
the system. Replica control algorithms are used to maintain
the consistency among these copies. One of these is the read-
one/write-all protocol. With this protocol an exclusive lock
need to acquire an exclusive lock from every copy of the data
item . For a shared lock to succeed, any one cop)' of the data
item has to be share locked. When transactions with conflicting
lock requests are initiated concurrently, they coL, ld I)e possibly
blocked due to a deadlock.
There are two major ways to evaluate the performance of
distributed systems: simulation and analysis. Simulation is a
conceptually tractable technique, but requires large colllputa-
tion time. On the other hand, analysis is computatio,_ally faster
but may not be tractable for all problems. In [4], Shyu and Li
proposed an elegant analysis model to evaluate the response
time and throughput of transactions in a non-replicated DDS.
Assuming exclusive locking (i.e., oniy write operationsl, they
model the queue of lock requests at an object as an M/M/i
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. With
shared lock and replications added into the picture, it is very
difficult to have a close model for it. Because of the limits.
tions of simulation and analysis, we develop a technique that
combines simulation and analysis.
This paper is organized as the follows. In Section 2, we de-
scribe the model used in our performance evaluation. In Section
3, we propose an evaluation technique. In Section 4, we illus-
trate the results. Finally, Section 5 has the conclusions.
2. Model
Our model has the following parameters:
* There are n nodes.
* There are d data items in a DDS.
• A data item may be located at exactly c number of nodes.
The dc data copies are uniformly distributed across the n
nodes.
• Each transaction accesses k data items.
a r is the read ratio. So among k data items to be accessed,
rk are accessed only for read operations, and the rest
are for read-write operations. Due to the read-one/write-
all replica control policy, a transaction must procure rk
shared locks for rk read operations and (I - r)kc exclusive
locks for the (1 - r)k read-write operations.
Each data item is equally likely to be accessed by a trans-
action.
Transaction arrivals into the system is a Poisson process
witll rate A.
The communication delay between any two nodes is ex-
ponentially distributed with mean f.
The average execution time of a transaction, once the
locks are obtained, is ,L
The deadlock mechanism is invoked every _" seconds.
After an abortion of a transaction, it takes an average of
w seconds for this transaction to be restarted.
, _ is the service rate of transactions.
|This research was supported in part by the NASA Langley Research
Center under ¢ontractl NAG-l-Ill4 and NAG-I-I t54
• b is the lock-holding time.
• Ac is the arrival rate at each data copy.
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3. Performance Evaluation Technique
Our technique consistsof two stages.In the firststage,tlle
average transaction response time and throughput are calcu-
latedby ignoring the deadlock. This isan iterativestep involv-
in S simulatior, and analysis. Ill tile secoud _tage, the proba-
bilities of transaction conflicts and deadlocks are COml,lted by
probability models. These probabilities are used, ill t_m_, to
compute the response time and throughput ill tile i)rt'sencc of
deadlocks.
Stage 1:
Initially, we assume that there are no lock conflicts I)etweeu
transactions. Each transaction has to procure rk shar,'d lock
on data copies and (1 - r)kc exclusive locks on data copies.
When a transaction has got all the lock grants from these- data
objects, it can go ahead with execution.
This procedure is summarized in the following _ steps.
1. Initialize lock-holding time(b) to be 1/#.
2. Given the totalrateof transactionarrival(A),tileshared
lock ratio(r), the number of data items(d), the nm'll|)er ol"
data items required by each tra,sacthm(/,') and lho mml-
bcr of replications(c), derive the arriwd rat,. a! ,.a,'h data
copy(At).
3. With the arrival rate at each data copy(Ae), the average
lock-holding time(b), and the transmission time(Q we can
simulate the queue at a data copy to arrivewait-time{w)
distribution.With thisdistributionwe can cak'ulatethe
response time of transactions.
4. With the average servicetime of trausactious(lh(),atl(l
the transmission time, we can derive a new h)ck.hohli,lg
time(Y).
5. Set b to this new lock-holding time bt.
6. Ifthe old and new lock-hohlingtinleare sulficicltilyclose.
stop the iteration.Otherwise, go back to st(,p3.
At the end of stage t the response time without tile consi(h'ra-
tion of transaction deadlocks is obtained.
Stage 2:
This stage considers transaction conflicts and computes the
deadlock probability. Here the probabilities of transaction dead-
lock and restart are computed. These are then used to compute
response time and throughput in the presence of deadlocks.
Assume there are two transactions T1 and T2. Let RS, WS
be the read and write sets of transactions respectively.
1. Let fs, be the probability that the readset of'l'! has i data
items overlapping with the writeset of T2, i.e. IRS(TI } n
WS(T2)I = i.
2. Let f% be the probability that given ]RS(TI)nWS(T2)I =
i, the writeset of TI has j data items overlaping wilh
the readset and writeset of T2, i.e. the i)rolmlfility that
lWS(Tt) n (Its('r'.,)u W_'('I'2))l= j.
Clearly,
699
(,;,,) _,-,+,,_
D, = _ "*-'/ (1)(:,)
/(,, = (__,_ (2)
_.k-rk]
It can also be noted that fb,fe,_ is tile probability that:
IRcad-set(Tl )N\Vrite-set(T2)l=i
A IWrite-set( T I )N( Write-set(T2)ORead-set(T2))l= j.
If PIV, i is the probability that T1 waits for T2,
PW. = pl + p2 - pl * p2 (3)
pt = t - [] -(I/2)'1' (4)
v2 = (t-(I/2)") (s)
where pl is the probability that T1 waits for T2 for shared locks
in readset
and p2 is the probability that T1 waits for T2 for exclusive locks
in writeset.
Probability that TI waits for T2 is now given by
mm(t,k-#) n,,(_- r.k-"|
I',,, = _ _ f#,fe,,l'W,, (6)
,=O ,1=0
With this probability of waiting and the formulas in [4] we can
calculate tile probability of a transaction deadlock, the prob-
ability of a transaction restart and the probability of a trans-
action to be blocked by other transactions. And with these
probabilities and the time between deadlock detection(r), we
can calculate tit(' response time with consideration of deadlock.
(Details are ometted here.)
4. Results
Using this technique, we obtained a number of interesting
results that illustrate the effect of deadlocks and number of
replications on database performance. These are summarized
in Figures l-5. We make the following observations.
• Transaction response times are quite sensitive to the ratio
of shared locks (Figure I and 2). Here, we compare the re-
sponse times when deadlocks are ignored (DI, computed in
Stage I) with those obtained when deadlocks are consid-
ered (DC, computed in Stage 2). The effect of deadlocks
is more predominant at higher transaction loads and with
smaller values of r. When r = 2/3, the effect of deadlocks
is not signilicant on response time.
• Ifw(, c,mq_are l"igur,' l aud 2 with Figure 3 aml 4, it cau
I)e ohscrvt.d that tilt' increase ill replications resultsiu the
larger response time when read ratio is smaller than [/3.
• Fig. 5 shows the response times with different replication
numbers, llere we can see that with both cases when
read ratio is 2/3 and 1/3, the response time increases as
the number of replications increases. But with read ratio
equals 1/3, tileincreasing rate is much smaller than that
with road ratio equals 2[:|.
5. Conclusions
In [4], Shyu and Li presented an elegant technique to eval-
uate the performance of distributed database systems in the
presence of deadlocks. Their technique assumed only exclusive
locks aud thus representing tile worst-case effects of deadlocks.
response
umc
(see)
response
time
(see)
response
time
(see)
2
1.8
16
14
12
1
0.8
06
7
C=2 41, ar= 1.00
k= 3 / &r = 0.67d = 200 +r 0.33
*r = 0.00
r =20 /
./ /i'= 0,2
= .
0 2 4 6
arrival mte(trans/sec) 2
Figure. 1 Comparison of response time with different
read ratio when deadlock is ignored.
2
18
1.6
14
12
1
0.8
06
c=2 / / =r= 1.00
• • = 0.67
k= 3 er = 0.33
d=200 Or = 0.00
r =20
m =2
t_= 0.2
= .
0 2 4 6
arrival rate(ttan_sec) ,1
Figure.2 Compari_n of response time with different
read ratio when deadlock is considered.
2
1B
16
14
1.2
t
05
0.6
c=3
k=3
d=200
r =20
ca, =2
[=0.2
S- 0.01
_ =r= 1.00
• • = 0.67
¢r = 0.33
¢r =0.00
m .........
0 2 4 6
arrival ram0zans/se¢) J.
Figure.3 CompQrison of response time with different
road ratio when deadlock is ignored.
rc_ponse
time
(see)
2
18
16
14
12
1
08
06
C=3
k:3
d= 200
T :20
ta =2
i-=0.2
f=0.01
_ Ir= 1.00
• r = 0.67
÷r = 0.33
Cr = 0.00
m ....... • -
0 2 4 6
arrival rate(trans/sec) ,l
Figure.4 Comparison of response time with diffcren!
read ratio when deadlock is ignored.
response
time
(so:)
2.2
2
1,8
1.6
1.4
12
1
0.8
k=6 JfDC ,r = 0.67
d = 1000 /_ • r = 0.33
=m //.DI
o_ -2 //
t*0.2 //
i.o.o, //
_=4
DC
DI
3 5
replication number c
Figure.5 Comparison ofresponsetimewithdilTerml
read ratiowithand withoutdeadlock.
De: Deadlock Considered.
Dh Deadlock Ignmed.
In this paper, we have extended their technique to combin¢_
ulation and analysis. And with this extended technique*ed_
both shared and exclusive locking and also replicationl i=_
model. We evaluated the the effect of number of data itemt./
number of data items accessed by each transaction, the r_
read operations o,t transaction response time and the nurr/_
replications. These results show the importance of consi&111
both shared and exclusive lock requests, the deadlotk
bilities as well as the number of replications of datal_¢ll_
response time evaluations.
700
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_q
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