Termination Detection Protocols for
Mobile Distributed Systems
Yu-Chee Tseng, Member, IEEE Computer Society, and Cheng-Chung Tan
AbstractÐThis paper studies a fundamental problem, the termination detection problem, in distributed systems. Under a wireless network environment, we show how to handle the host mobility and disconnection problems. In particular, when some distributed processes are temporarily disconnected, we show how to capture a weakly terminated state where silence has been reached only by those currently connected processes. A user may desire to know such a state to tell whether the mobile distributed system is still running or is silent because some processes are disconnected. Our protocol tries to exploit the network hierarchy by combining two existing protocols together. It employs the weight-throwing scheme [9], [16], [21] on the wired network side, and the diffusion-based scheme [5], [13] on each wireless cell. Such a hybrid protocol can better pave the gaps of computation and communication capability between static and mobile hosts, thus more scalable to larger distributed systems. Analysis and simulation results are also presented. Index TermsÐDistributed computing, distributed protocol, mobile computing, operating system, termination detection, wireless network.
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1 I
NTRODUCTIONO
NE major breakthrough in computer communicationrecently is the extension from wired to wireless transmission. Wireless communication products ranging from LAN, MAN, to WAN are available commercially [7], [8]. Another breakthrough in computing devices is the maturity of light-weight, economic, hand-held laptop and palmtop computers. This has made mobile computing (or nomadic computing) possible [11]. Users can carry computers (or mobile hosts) while moving around and remain in touch with networks.
Designing a distributed system with wireless commu-nication components does pose some new challenges. First, distributed processes in mobile hosts have mobility. Second, mobile hosts are inherently weaker in computing capability than fixed hosts. Third, wireless communication has less (about an order or two) bandwidth and higher error rate compared to wired communication. These have interested a lot of researchers. Issues that have been considered on mobile distributed environments include message causal ordering [2], [18], [24], fault tolerance [1], distributed snapshot [23], and distributed checkpointing [12], [19].
In this paper, we study one fundamental problem, the termination detection problem, in a mobile distributed system. As a basic problem in operating system design, termination detection refers to the necessity of determining whether a set of distributed processes has entered a ªsilentº status where all processes are idle and no further computation is
possible, taking the unpredictable message delays into account [20]. This problem was first identified by Dijkstra and Scholten [5], which has then inspired a lot of studies [4], [6], [9], [13], [14], [16], [17], [21], [22]. It has applications in diffusion computation [5], distributed workpool [15], and distributed garbage collection. It also serves a part in checking stable states (such as deadlock and token loss) in a distributed system [10], [20].
Under a wireless network environment, we propose a termination detection protocol that can handle the host mobility and disconnection problems. We assume that the mobility problem is not directly supported by the under-lying protocol, and should be taken care of by the termination detection protocol. In particular, when some distributed processes are temporarily disconnected, we newly define a weakly terminated state where ªsilenceº has been reached only by those currently connected processes in the distributed system. Our protocol can catch such a state so that a user will not be caught in the dilemma of wondering whether the mobile distributed system is still running or is silent because some mobile processes are disconnected. To exploit the network hierarchy, our protocol is in fact a combination of two existing protocols designed for static distributed systems. It employs the weight-throwing scheme [9], [16], [21] on the wired network side, and the diffusion-based scheme [5], [13] on each wireless cell. It is shown that such a hybrid approach can better pave the gaps of computation and communication capability between static and mobile hosts, thus more scalable to larger distributed systems. Through analyses and simula-tions, we demonstrate that our protocol places less demand of space and computing power on mobile hosts and of communication bandwidth on wireless links.
The rest of this paper is organized as follows: In Section 2, the distributed termination detection problem is formally defined and two existing protocols are reviewed. Our hybrid protocol is presented in Section 3, followed by . Y.-C. Tseng is with the Department of Computer Science and Information
Engineering, National Chiao-Tung University, Hsin-Chu 30050, Taiwan. E-mail: [email protected].
. C.-C. Tan is with the Department of Computer Science and Information Engineering, National Central University, Chung-Li 32054, Taiwan. E-mail: [email protected].
Manuscript received 14 July 1999; revised 26 Sept. 2000; accepted 7 Feb. 2001.
For information on obtaining reprints of this article, please send e-mail to: [email protected], and reference IEEECS Log Number 110239.
comparisons and simulation results in Section 4. Conclu-sions are drawn in Section 5.
2 P
RELIMINARIES ANDR
EVIEWS2.1 Distributed Termination Detection
A distributed system consists of a set of autonomous processes S fP1; P2; ; Png which cooperate with each other
to complete a job. Processes can communicate with each other by message-passing. Logically, from each Pi to each
Pj, there is a communication channel Ci;j. A process may
switch between two states: active and idle. A process, when performing some computation, is said to be in the active state. An active process is free to send/receive messages and may become idle spontaneously. On idle state, a process does not perform any computation, but can passively receive messages, on which event it becomes active immediately and starts computations. For distinction, computation carried out and messages transmitted by the system are called basic computation and basic messages, respectively.
A distributed system is said to be terminated iff 1) Pi is
idle and 2) Ci;jis empty, for all 1 i; j n. (Condition 2 is
necessary because message delays are unpredictable and any ªhiddenº message will wake the system up later.) When terminated, no distributed process can become active and perform any further computation. Due to the variation of processor speeds and the unpredictability of message delays, detecting such a status is usually nontrivial. In the literature, this is known as the distributed termination detection problem. Extra messages (typically called control messages) are sent and/or extra information is associated with basic messages to detect such a state.
2.2 Review: The Diffusion-Based Scheme
The diffusion-based scheme [5], [13] detects termination following the expansion of the basic computation. Below, we present the version by [13]. The basic idea is to maintain a logical tree connecting all active (and perhaps some idle) processes. The basic computation is assumed to start from process P1, which is regarded as the root of the tree. The
tree may expand or shrink dynamically. When the tree shrinks to P1 only and P1 is idle, the system is terminated.
The tree is maintained by the following data structures in each process Pi:
. pari: the parent of Pi. Initially, it is NULL.
. ini1::n: an array of integers, where inij is the
number of basic messages that have been received from Pj but have not been acknowledged. Initially,
this value is 0.
. outi: an integer indicating the number of basic
messages that have been sent by Pi but have not
been acknowledged. Initially, outi 0.
The detection scheme consists of four event-driven rules of the format ªevent ) action,º where action is the program segment to be executed when event occurs.
A1. On Pi sending a basic message to another process
) outi: outi 1;
A2. Pi receiving a basic message from Pj )
inij : inij 1;
if (pari NULL ^ i 6 1 then pari: j;
A3. On Pi turning idle )
reply minor(i);
if outi 0 then reply major i;
A4. Pi receiving an ACK k )
outi: outiÿ k;
if (Pi is idle) ^ (outi 0) then reply major i;
For the tree to shrink, acknowledgments should be sent. We call a message a major message if it was from Pi's
parent, otherwise, it is a minor message. Minor messages can be acknowledged whenever Pi turns idle, but major
messages can only be acknowledged when Piis idle and all
Pi's outgoing messages have been acknowledged. The
following procedures are for this purpose: Procedure reply minor i
begin
for each j 6 pari such that inij 6 0 do
else
send an ACK inij to Pj;
inij : 0;
end for; end.
Procedure reply major i begin
if (i = 1) then report termination
send an ACK inipari to process pari;
inipari : 0;
pari: NULL;
end if; end.
2.3 Review: The Weight-Throwing Scheme
According to the problem definition, to detect termination, we mainly need to collect two kinds of information: 1) the idleness of processes and 2) the emptiness of communica-tion channels. The weight-throwing scheme [9], [16] collec-tively represents them using one notion called weight. A weight is simply a real number, which can either be held by a process or be appended at a basic message while transmitted.
Initially, a predesignated process Pc (called weight
collector) holds a weight wc 1 and all other process
Pi; i 6 c; holds a weight wi 0. Process Pc is typically
the one who starts the basic computation. It also serves as the central coordinator for termination detection. The protocol is derived based on a weight-invariant concept. It consists of four rules:
B1. On Pi sending a basic message to another process )
partition wiinto two positive reals x and y such that
x y wi;
append the weight x to the basic message; wi: y;
B2. On Pjreceiving a basic message with weight x )
B3. On Pi; i 6 c; switching from active to idle )
send a weight-report message WGT wi to Pc;
wi: 0;
B4. On Pc receiving WGT wi from Pi ) wc: wc wi;
Throughout, two important invariants are preserved by the protocol:
1. Every active process holds a positive weight. Every in-transit basic and control message also holds a positive weight.
2. The sum of weights held by Pc, all active processes,
all in-transit basic, and all in-transit control mes-sages, is equal to 1 at the same time.
Therefore, when Pcbecomes idle and finds a weight of 1 at
its hand, no processes can be active and no messages can be in-transit. So termination of the system can be announced. 2.4 Discussion
Below, we compare the strength and weakness of these two schemes, intending to motivate the work (a hybrid protocol) in this paper.
Space Complexity. The diffusion-based scheme needs an array of size O n (array in ) in each process, where n is the size of the distributed system, while the weight-throwing scheme has a space complexity of O 1 in each process. So the latter is more scalable in system size.
Computing Compelxity. Integers are used to maintain the tree T in the diffusion-based scheme, while floating numbers are used to represent weights in the weight-throwing scheme. Note that the regular hardware-sup-ported floating-point arithmetic (which usually incurs truncating/rounding errors) should not be used with the weight-throwing scheme. Weights must be lossless and must be precisely represented to ensure correctness. This implies a software-emulated floating-point arithmetic and sometimes weight borrowing to take care of the repeated weight-split and combine problems [9], [16]. The weight calculation is computationally more costly.
Time Complexity. Let's define detection delay to be the time that a protocol takes to correctly report the termination status after a distributed system is terminated. In the diffusion-based scheme, this is reflected by the height of T and thus the detection delay is O n. The delay for the weight-throwing scheme is O 1 as weights are always sent directly to the weight collector.
Communication Bandwidth. Both schemes were proved to be asymptotically optimal in terms of the number of control messages sent per basic message [13]. Looking in more details, we see that the weight-throwing scheme needs to append a weight on each basic message while there is no such cost for the diffusion scheme. However, counting the number of control messages being sent each time a mobile process turns idle, we see that exactly one WGT message is sent by the weight-throwing scheme, while the diffusion scheme will send nmajand nminACK 's
to acknowledge major and minor messages, respectively, where nmaj 0 or 1, nmin 0, but nmaj nmin 1.
3 A H
YBRIDT
ERMINATIOND
ETECTIONP
ROTOCOL3.1 System Model
A distributed system consists of a set of processes fP1; P2; . . . ; Png. For distinction, a process Pi on a static
host will be called a static process and denoted as Ps
i and that
on a mobile host called mobile process and denoted as Pm i .
We consider a network architecture consisting of a wired part as the backbone connecting to a set of base stations fPb
1; P2b; . . . ; Pmbg. Communications to and from a mobile
process must be relayed by a base station. The transmission range covered by a base station is called a cell. Each base station serves as a mobile-support station (MSS) [1], [2], [3], [19], [24] and can cooperate with the distributed system to detect the terminated status of the system. In general, any Ps
i, Pim, and Pib can be referred to as a ªprocess.º Message
transmission between any two processes is reliable, but unpredictable, and follows a FIFO (first-in-first-out) model. A mobile process can roam around any base station, and may roam off its current base station and become temporarily disconnected. A disconnected process can still perform computation, but all communication jobs to and from it should be suspended for future processing. We thus define two kinds of termination statuses as follows: Definition 1. A distributed system is strongly terminated if all
processes are idle and there is no in-transit basic message. It is called weakly terminated if such a state is reached by all processes except disconnected processes.
Knowing a system has entered a weakly terminated state is better than keeping a user waiting uncertain of the system's current state. (Still running? Or some mobile hosts being disconnected?) Our yet-to-be-presented protocol can even determine which processes have reached such a state. 3.2 Basic Idea and Data Structures
Our protocol is a hybrid of the diffusion-based and weight-throwing schemes. On each wireless cell, the diffusion-based scheme is used. While on the wired networks, the weight-throwing scheme is used. The base stations work in between to bridge these two protocols together. Our intention is to impose less burden (including storage, computation, and communication) on mobile processes, but not to sacrifice efficiency in the termination detection job. Intuitively, the weight-throwing scheme is better in both space and detection latency when the network scale is large, but it has to deal with real numbers. The diffusion scheme deals with only integer and, when applied on a wireless cell, will be a fine choice because all mobile hosts within a cell can talk to each other directly in one-hop. This is why we make such combinations.
As the weight-throwing scheme is used on the wired network, each static process Ps
k should keep a weight wk.
We assume that there is a special static process called Ps c
serving as the weight collector (alternatively, we can let some base station Pb
c play this role). Process Pcshas an initial
weight of wc 1. It also serves as the starter of the
distributed computation (or, any process intending to begin a distributed computation cannotify Ps
c to ªstartº the
addition, to handle the mobility issue, Ps
c needs three new
variables:
. : the set of temporarily disconnected processes. . : the total weight held by the processes in . . outc1::n: to store the numbers of unacknowledged
basic messages for those temporarily disconnected processes in .
On each mobile process Pm
j , a simplified diffusion-based
scheme is used. Only one variable is kept by Pm j :
. inj: the number of basic messages that have been
received (from base stations) but have not been acknowledged.
Note that the pointer to Pm
j 's parent and the variable out
used in the original diffusion-based scheme are not needed any more. Further, the array inj1::n is now reduced to a
scalar. Intuitively, this is because a mobile process always regards its current base station as its parent, to which all communications will be addressed.
Each base station Pb
i needs to run both protocols and,
thus, will keep the following variables: . wi: the weight Pib holding at hand.
. i: the set of mobile processes currently supported
by Pb i.
. outi1::n: an array of integers, where outij is the
number of basic messages that have been sent to Pm
j 2 i, but have not been acknowledged.
Note that on the contrary, the scalar outi in the original
scheme is now extended to an array. Intuitively, this is for the purpose of detecting the weakly terminated state.
Some of these variables are illustrated and related by messages in Fig. 1. The message types to be used in our protocol are listed below.
. M: a basic message; if M is appended with a weight w, we will write M w.
. WGT w: a message reporting a weight of w.
. ACK k: an acknowledgment of k basic messages.
. HF: handoff-related message which contains four
subtypes: HF:req; HF:ind; HF:reply; and HF:ack.
. DISC Pm
k ; i; w: a message associated with a weight
w to report that a mobile process Pm
k is disconnected
and has i unacknowledged basic messages.
3.3 The Protocol
3.3.1 Static and Weight-Collecting Process Each static process, including the weight collector Ps
c, runs
the original weight-throwing rules B1±B4 in Section 2.3. (How Ps
c announces termination is in Section 3.3.7.)
3.3.2 Mobile Processes Each mobile process Pm
j runs a simplified diffusion-based
scheme by always assuming its current base station as its parent and imagining all basic messages as being issued from or addressed to the base station.
C1. On Pm
j sending a basic message to another process )
do nothing; C2. On Pm
j receiving a basic message from its base station
) inj: inj 1;
C3. On Pm
j turning idle ) reply();
Compared to the original diffusion-based scheme in Section 2.2, A1 in fact turns to a null action (C1 is presented here only for clarity), A2 is simplified, and A3 and A4 are merged into a simpler rule. There is no concept of major or minor messages within a cell, so reply major and reply minor are merged into a simpler reply as follows: Procedure reply
begin
Send an ACK inj to its base station;
inj: 0;
end.
3.3.3 Base Stations Each base station Pb
i serves as a bridge between the wired
and wireless networks. It first tries to detect the termination of all its local mobile processes based on the diffusion protocol. On finding this being true, it reports to Ps c
following the weight-throwing protocol: D1. On Pb
i receiving an M x from the wired networks
destined to a Pm j 2 i)
wi: wi x;
outij : outij 1;
Forward M (without appending x) to Pm j ;
D2. On Pb
i receiving an M from a local mobile process 2 i
destined to a process Pj)
if Pj2 i, then / for a local mobile process /
outij : outij 1;
Forward M to Pm
j ;
else / for a nonlocal process /
Forward M wi=2 to Pj;
wi: wi=2;
end if; D3. On Pb
i receiving an ACK k from a Pjm2 i )
outij : outij ÿ k;
if (outix 0 for all Pxm2 i) then
Send a WGT wi to the weight collector Pcs;
wi: 0;
end if;
The above rules guarantee two important properties: Property 1. outij 0) (Pjm2 i is idle) ^ (there is no
in-transit basic message between Pb
i and Pjm).
Property 2. wi 0) (each Pjm2 i is idle) ^ (there is no
in-transit basic message between Pb
i and each Pjm2 i).
To prove Property 1, first observe that when outij 0, all
basic messages sent to Pm
j have been acknowledged, so Pjm
must be idle and the channel from Pb
i to Pjmis empty. By C3,
when Pm
j turns idle, the last message sent out by it must be
an ACK . As the channel is FIFO, this ACK will flush all basic messages sent from Pm
j to Pib. So the channel from Pjm
to Pb
i must be empty and this proves Property 1. Property 2
can be proven by examining each Pm
j 2 i based on
Property 1. It follows that D3 will lead to Property 2. 3.3.4 Hand-Off of Mobile Processes
When a mobile process Pm
k is handed off from its current
base station Pb
i to another Pjb, the following rules are used:
Fig. 2 illustrates these steps. E1. On Pm
k intending to be hand-off from Pibto Pjb )
Pm
k sends a HF:req Pib to Pjb and waits for Pjb's
HF:ack until it times out; Pm
k stops sending and receiving any message until
HF:ack is received; E2. On Pb
j receiving HF:req Pib from Pkm) Pjbsends a
HF:ind Pm
k to Pib;
E3. On Pb
i receiving HF:ind Pkm from Pjb )
i: iÿ fPkmg;
if (outik 0) then / Pkmidle /
Send a HF:reply Pm
k ; outik; 0 to Pjb;
else if (outix 0 for all Pxm2 i) then / processes
in i idle /
Send a HF:reply Pm
k ; outik; wi to Pjb;
wi: 0;
else / some processes in i active /
Send a HF:reply Pm
k ; outik; wi=2 to Pjb;
wi: wi=2;
end if; E4. On Pb
j receiving HF:reply Pkm; outik; w from Pib )
j: j[ fPkmg;
outjk : outik;
wj: wj w;
Send a HF:ack to Pm k ;
Note that the above four steps may not always complete successfully. That is, Pm
k , after performing E1, may leave
base station Pb
j before the HF:ack returns. Thus, a timeout
parameter should be set to deal with this problem. In this case, we regard that Pm
k has been handed off to Pjb, although
Pm
k has not been committed of this event. Subsequent steps
E2 and E3, which only involve static processes, can complete successfully and, thus, migrate Pm
k 's data
struc-ture from Pb
i to Pjb. After the timeout period, if Pkm fails
receiving HF:ack (due to mobility), it is free to hand-off to another base station by restarting E1. It should indicate its original base station as Pb
j instead of Pib. This will prevent
Pm
k from being blocked due to high mobility. Also note that
rule E1 ensures that Pm
k can only exchange messages with a
base station that is formally committed (by HF:ack) as its current base station. Hence, the message exchange history will be recorded correctly (by array out ) and mobility will not disrupt our protocol.
3.3.5 Temporary Disconnection and Rejoining of Mobile Processes
A reasonable assumption for disconnection is that such a status should be determined by each mobile host and base station autonomously. Specifically, when a mobile process finds that it is not connected to any base station, it can decide to enter a disconnected mode at its own will. Similarly, a base station determines that a mobile process has entered a disconnected mode if it finds 1) that it cannot hear from the process and 2) that there is no hand-off request from this mobile process for a predefined time.
A disconnected process should stop any message exchange (but local computation can continue). On the other side, a base station can return the disconnected process's data structure to the weight collector (in hope of reaching a conclusion that the distributed system is weakly terminated).
F1. On a Pm
k deciding to enter a disconnected mode ) Pkm
suspend all message exchange; F2. On a Pb
i deciding that a Pkm2 i has entered a
disconnected mode ) i: iÿ fPkmg;
if (outik 0) then / Pkmidle /
Send a DISC Pm
k ; outik; 0 to Pcs;
else if (outix 0 for all Pxm2 i) then / processes
in i idle /
Send a DISC Pm
k ; outik; wi to Pcs;
wi: 0;
else / some processes in i active /
Send a DISC Pm
k ; outik; wi=2 to Pcs;
wi: wi=2;
end if;
F3. On Ps
c receiving DISC Pkm; outik; w )
: [ fPm k g;
outck : outik;
: w;
F2 manages the weights based on different combinations of processes' states. F3 appends the received weight to . Depending on the value of , the weight collector will try to determine the strongly/weakly terminated state of the system (refer to Section 3.3.7).
In our protocol, disconnection is handled very similar to
hand-off. When a mobile process Pm
k in a disconnected
mode hears any base station again, it can enter a connected mode again and execute the hand-off rule, E1, in the previous section to rejoin the system. Suppose Pm
k 's original
and new base stations are Pb
i and Pjb, respectively. On
hearing Pm
k 's hand-off request, if Pib still has Pkm's data
structure (i.e., Pm
k 2 i), then the normal hand-off
proce-dure takes action (by executing rules E2-E4). Otherwise, if Pm
k 62 i, the hand-off request will be forwarded to the
weight collector Ps
c and the following rule will be executed:
F4. On Ps
c receiving the forwarded HF:ind Pkm from Pib)
if (Pm
k 2 ) then
: ÿ fPm k g;
if (outck 0) then Send a
HF:reply Pm k ; outck; 0 to Pjb; else / Pm k active / Send a HF:reply Pm k ; outck; =2 to Pjb; : =2; if ( ;) then wc: wc ; end if; end if;
Note that the ªif ( ;) then ...º statement is to ensure that no weight is left in if there is no disconnected process. Also, note that the above indices, i and j, do not have to be different. The modification is straight forward: We simply let Pb
i play both roles.
Finally, when the HF:reply from the weight collector arrives at base station Pb
j, rule E4 will take action like a
normal hand-off. A note similar to the hand-off procedure is that the above steps may not always complete successfully after Pm
k performs E1. Still, we regard that Pkm has been
hand-off to Pb
j, although Pkmhas not been committed of this
event. No message exchange should be done with Pm k in the
meantime. The subsequent steps, which are on wired networks, will eventually deliver HF:reply to Pb
j. If by the
time Pm
k has migrated to another base station or become
disconnected again, Pb
j simply serves as Pkm's current base
station and performs the above rules at its own determina-tion. This ensures that temporary disconnection will not disrupt our protocol.
3.3.6 Dangling Messages
Dangling messages are those that cannot be delivered due to disconnection or host mobility. Since dangling messages may be delivered at any time later, care must be taken to avoid terminated states being falsely announced.
Dangling messages could exist in a mobile host when it is experiencing hand-off or disconnection. Since we always require that a base station obtain a mobile host's data
structure before exchanging any message with it (observe the guarded conditions in D1-D3), these dangling messages will be kept locally in the mobile process until a formal hand-off is committed. So the message exchange history is always correctly recorded.
Dangling messages could also exist in a base station or a static process if the messages are destined to a hand-off or disconnected mobile process. Ensured by the weight-throwing rules, each process holding a dangling message must have a nonzero weight at hand. A reasonable approach is to forward dangling messages to the weight collector as if they are destined to it. A nonzero weight should be appended to each such message. The weight collector includes these weights into and queues these messages for future processing:
G1. On Ps
c receiving a dangling message carrying a weight
x ) : x; G2. On Ps
c sending a dangling message M to a reconnected
mobile process ) Append a weight =2 to M; : =2;
if (dangling message list becomes empty) then wc: wc ;
: 0; end if;
3.3.7 Announcing Termination The weight collector Ps
c can announce that the distributed
system has entered a strongly or weakly terminated state once it has collected a sufficient weight of 1.
H1. On Ps
c finding wc 1 )
if ( > 0) then announce ªweakly terminated (excluding processes in )º else announce ªstrongly terminatedº;
A weakly terminated state guarantees that all currently connected processes are idle and there are no in-transit basic or dangling messages. It would be easier to design the application programs on top of the termination detection protocol because without the weight collector's permit (rule F4), no further computation in a weakly terminated system is possible. There are two possibilities for a weakly terminated state: 1) some dangling basic messages at Ps
c's
hand and 2) some disconnected processes not acknowl-edging receipt of basic messages yet. In either case, the weight collector will have a nonzero . On the other hand, note that the system can be strongly terminated even if some mobile processes are disconnected ( 6 ;), but the whole system is terminated for sure.
4 C
OMPARISONS ANDS
IMULATIONR
ESULTSA comparison based on a nonmobile system is in Table 1 (i.e., we assume that there are no host mobility and disconnection problems for the diffusion-based and weight-throwing schemes). Since we assume that mobile hosts are inherently weaker than static hosts, the compar-ison focuses on the space and computation complexity on mobile processes and the wireless bandwidth consumed.
ªSpaceº indicates the size of data structures used by each protocol. ªComputationº indicates the data types to be processed for the purpose of termination detection (weight representation should be lossless, refer to Section 2.4). ªDetection delayº is to count the maximum number of communication hops happening on the wireless links for our protocol to report termination once the system is terminated (the communication on wired links are considered to be much faster and, thus, is not counted in this metric). ªControl messageº is to count the number of control messages (ACK or WGT ) sent on wireless links each time when a mobile process turns idle. Note that our cost is 1 since we delegate the weight collector to a static process whereas the costs for the diffusion and weight-throwing schemes are doubled since each control message has to traverse on two wireless links.
A simulator was also developed to calculate the exact the wireless bandwidth consumed for the purpose of termina-tion detectermina-tion. We simulated a distributed system with m base stations, with m ranging from 1 to 10. Each base station owns four mobile hosts, each running one distributed process. As our focus is on the wireless part, no static processes were simulated. One process started the dis-tributed system by injecting m basic messages into the system. On receiving a basic message, a mobile host will become active for A time units, where A is uniformly distributed in 1; 49 with a mean of 25 time units. While active, a process could generate a new basic message every M time units, where M is also a random variable with a certain mean. The destination of a basic message was randomly selected from one of the other mobile processes. The distributed system was run until it naturally terminated or a preset timer of 2,000 expired.
Fig. 3 shows the number of control messages traveling on wireless links by the three protocols. We varied the ratio
A=M (among 1=4; 1=2; 1; 2; 3; . . . ; 10) at different system sizes (m 2; 5; 8). Because mobility cannot be handled by the other two protocols, hand-off and disconnection were not simulated. The weight-throwing scheme uses about two times the control messages used by the hybrid scheme. The diffusion-based scheme has similar performance as ours at low A=M ratios, but is getting worse and worse when the A=M ratio gradually increases over 1/2. Both weight-throwing and hybrid protocols are quite insensitive to the A=M ratio.
An important factor that has been ignored in the previous simulation is the extra weight that has to be carried by each basic message in the weight-throwing scheme. We adopted a simple assumption that each ACK k costs 4 bytes (for an integer) and each WCT x and basic message costs 8 bytes (for a real number). Byte counts are important for systems frequently delivering very short messages. Fig. 4 shows the average number of bytes required by a mobile host per unit time under different conditions (the other protocol overheads, such as packet header and error-checking code, which should be the same for different protocols, are not accounted in the simulation figures). Under this metric, the weight-throwing scheme is always most costly.
We also compare the three protocols by varying the system sizes (m 1::10) at A=M 2; 5; 8. The results are shown in Fig. 5 and Fig. 6. We observe that the curves for the weight-throwing and hybrid schemes are both insensi-tive to the system size, but the curves for the diffusion-based scheme are slightly going upward as the system size increases. So the weight-throwing and hybrid schemes are more scalable to systems sizes.
TABLE 1
Comparison of Existing Hybrid and Our Hybrid Termination Detection Protocols for Mobile Processes
5 C
ONCLUSIONSWith the emergence of wireless networks, many distributed protocols well suited for static hosts have to be reevaluated for their appropriateness on wireless networks. Host mobility and disconnection problems are particularly important issues to be considered. In this paper, we have shown how to handle these problems for the termination detection problem. A newly defined weakly terminated state is provided for users to tell whether a mobile distributed system is still running or is silent because some processes are disconnected. By exploit the network hierarchy, our hybrid termination detection protocol can take advantage of the short detection delays of the weight-throwing scheme on the wired networks and the simplicity and bandwidth-efficient properties of the diffusion-based scheme on each wireless cell. It demands less space, computation, and wireless bandwidth on mobile processes and, thus, is more favorable.
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CKNOWLEDGMENTSThis research is supported by the Ministry of Education, ROC, under grant 89-H-FA07-1-4.
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Fig. 6. Number of bytes consumed at different system sizes.
Fig. 5. Number of control messages consumed at different system sizes. Fig. 4. Number of bytes consumed at different A=M ratios.
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Yu-Chee Tseng received the BS and MS degrees in computer science from the National Taiwan University and the National Tsing-Hua University in 1985 and 1987, respectively. He worked for the D-LINK Incorporated as an engineer in 1990. He obtained the PhD degree in computer and information science from Ohio State University in January of 1994. From 1994 to 1996, he was an associate professor at the Department of Computer Science, Chung-Hua University. He joined the Department of Computer Science and Information Engineering, National Central University in 1996 and has become a professor since 1999. Since Aug. 2000, he has been a professor at the Department of Computer Science and Information Engineering, National Chiao-Tung University, Taiwan. He served as a program committee member for the International Conference on Parallel and Distributed Systems, 1996, the International Conference on Parallel Processing, 1998, the International Conference on Distributed Comput-ing Systems, 2000, and the International Conference on Computer Communications and Networks 2000. He was a workshop cochair of the National Computer Symposium, 1999. His research interests include wireless communication, network security, parallel and distributed computing, and computer architecture. He is a member of the IEEE Computer Society and the Association for Computing Machinery.
Cheng-Chung Tan received the BS and MS degrees in computer science from Tamkang University and National Central University in 1997 and 1999, respectively. He has served as an engineer at the Institute for Information Industry in Taiwan since 2000. His currently working on embedded operating systems and IA products. His research interests include mobile computing, networking protocol, and operating system.
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