A hybrid solution of fork/join synchronization in parallel queues
A new analysis technique, dynamic-bubblesort analysis, is introduced for general K-queue first-in-first-out HFJ (homogenous fork/join queuing) systems of K/spl ges/2 . The dynamic-bubblesort model dynamically sorts the branches of the queues based on the number of the tasks waiting for synchronizati...
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| Published in | IEEE transactions on parallel and distributed systems Vol. 12; no. 8; pp. 829 - 845 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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New York
IEEE
01.08.2001
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Abstract | A new analysis technique, dynamic-bubblesort analysis, is introduced for general K-queue first-in-first-out HFJ (homogenous fork/join queuing) systems of K/spl ges/2 . The dynamic-bubblesort model dynamically sorts the branches of the queues based on the number of the tasks waiting for synchronization in each branch. Jobs arrive with mean rate /spl lambda/ and a general arrival distribution. Upon arrival, a job forks into K tasks. Task k, k=1, 2, ..., K, is assigned to the kth queuing system, which is a first-in-first-out server with a general service distribution and an infinite capacity queue. A job leaves the HFJ system as soon as all its tasks complete their service. In other words, tasks corresponding to the same job are joined before departing the HFJ system. We obtain a general and simple hybrid solution which combines analysis and simulation for the mean response time that we denote by T/sub K/. We obtain a very simple (as a function of T/sub 1/ and T/sub 2/ only) and general upper bound expression for T/sub K/ and we get an exact relationship between the cases for K=2 and 3. We evaluate our results by simulating 2, 3, ..., 99, and 100 queues for p=0.1, 0.2, ...0.8, and 0.9, each for four different HFJ cases, where /spl rho/=/spl lambda///spl mu/ and /spl mu/ is the average task service rate for a server. The maximum absolute offset for our hybrid solutions from all the simulations is less than 0.33 percent (1/300), which is a reasonable error ratio for simulation. The maximum offset for our upper bounds over all the simulations is 21 percent. |
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| AbstractList | A new analysis technique, dynamic-bubblesort analysis, is introduced for general K-queue first-in-first-out HFJ (homogenous fork/join queuing) systems of K greater than or equal to 2. The dynamic-bubblesort model dynamically sorts the branches of the queues based on the number of the tasks waiting for synchronization in each branch. Jobs arrive with mean rate lambda and a general arrival distribution. Upon arrival, a job forks into K tasks. Task k, k = 1, 2,..., K, is assigned to the kth queuing system, which is a first-in-first-out server with a general service distribution and an infinite capacity queue. A job leaves the HFJ system as soon as all its tasks complete their service. In other words, tasks corresponding to the same job are joined before departing the HFJ system. We obtain a general and simple hybrid solution which combines analysis and simulation for the mean response time that we denote by T sub(K). We obtain a very simple (as a function of T sub(1) and T sub(2) only) and general upper bound expression for T sub(K) and we get an exact relationship between the cases for K = 2 and 3. We evaluate our results by simulating 2, 3,..., 99, and 100 queues for rho = 0.1, 0.2,..., 0.8, and 0.9, each for four different HFJ cases, where rho = lambda / mu and mu is the average task service rate for a server. The maximum absolute offset for our hybrid solutions from all the simulations is less than 0.33 percent (1/300), which is a reasonable error ratio for simulation. The maximum offset for our upper bounds over all the simulations is 21 percent. Also, we compare our results with three recent papers. Task k, k=1, 2, ..., K, is assigned to the kth queuing system, which is a first-in-first-out server with a general service distribution and an infinite capacity queue. A new analysis technique, dynamic-bubblesort analysis, is introduced for general K-queue first-in-first-out HFJ (homogenous fork/join queuing) systems of K 2 . The dynamic-bubblesort model dynamically sorts the branches of the queues based on the number of the tasks waiting for synchronization in each branch. Jobs arrive with mean rate lambda and a general arrival distribution. Upon arrival, a job forks into K tasks. Task k, k=1, 2, ..., K, is assigned to the kth queuing system, which is a first-in-first-out server with a general service distribution and an infinite capacity queue. A job leaves the HFJ system as soon as all its tasks complete their service. In other words, tasks corresponding to the same job are joined before departing the HFJ system. We obtain a general and simple hybrid solution which combines analysis and simulation for the mean response time that we denote by T(K). We obtain a very simple (as a function of T(1) and T(2) only) and general upper bound expression for T(K) and we get an exact relationship between the cases for K=2 and 3. We evaluate our results by simulating 2, 3, ..., 99, and 100 queues for p=0.1, 0.2, ...0.8, and 0.9, each for four different HFJ cases, where rho=lambda/mu and mu is the average task service rate for a server. The maximum absolute offset for our hybrid solutions from all the simulations is less than 0.33 percent (1/300), which is a reasonable error ratio for simulation. The maximum offset for our upper bounds over all the simulations is 21 percent A new analysis technique, dynamic-bubblesort analysis, is introduced for general K-queue first-in-first-out HFJ (homogenous fork/join queuing) systems of K greater than or equal to 2 . The dynamic-bubblesort model dynamically sorts the branches of the queues based on the number of the tasks waiting for synchronization in each branch. Jobs arrive with mean rate lambda and a general arrival distribution. Upon arrival, a job forks into K tasks. Task k, k=1, 2, ..., K, is assigned to the kth queuing system, which is a first-in-first-out server with a general service distribution and an infinite capacity queue. A job leaves the HFJ system as soon as all its tasks complete their service. In other words, tasks corresponding to the same job are joined before departing the HFJ system. We obtain a general and simple hybrid solution which combines analysis and simulation for the mean response time that we denote by T sub(K). We obtain a very simple (as a function of T sub(1) and T sub(2) only) and general upper bound expression for T sub(K) and we get an exact relationship between the cases for K=2 and 3. We evaluate our results by simulating 2, 3, ..., 99, and 100 queues for p=0.1, 0.2, ...0.8, and 0.9, each for four different HFJ cases, where rho = lambda / mu and mu is the average task service rate for a server. The maximum absolute offset for our hybrid solutions from all the simulations is less than 0.33 percent (1/300), which is a reasonable error ratio for simulation. The maximum offset for our upper bounds over all the simulations is 21 percent A new analysis technique, dynamic-bubblesort analysis, is introduced for general K-queue first-in-first-out HFJ (homogenous fork/join queuing) systems of K/spl ges/2 . The dynamic-bubblesort model dynamically sorts the branches of the queues based on the number of the tasks waiting for synchronization in each branch. Jobs arrive with mean rate /spl lambda/ and a general arrival distribution. Upon arrival, a job forks into K tasks. Task k, k=1, 2, ..., K, is assigned to the kth queuing system, which is a first-in-first-out server with a general service distribution and an infinite capacity queue. A job leaves the HFJ system as soon as all its tasks complete their service. In other words, tasks corresponding to the same job are joined before departing the HFJ system. We obtain a general and simple hybrid solution which combines analysis and simulation for the mean response time that we denote by T/sub K/. We obtain a very simple (as a function of T/sub 1/ and T/sub 2/ only) and general upper bound expression for T/sub K/ and we get an exact relationship between the cases for K=2 and 3. We evaluate our results by simulating 2, 3, ..., 99, and 100 queues for p=0.1, 0.2, ...0.8, and 0.9, each for four different HFJ cases, where /spl rho/=/spl lambda///spl mu/ and /spl mu/ is the average task service rate for a server. The maximum absolute offset for our hybrid solutions from all the simulations is less than 0.33 percent (1/300), which is a reasonable error ratio for simulation. The maximum offset for our upper bounds over all the simulations is 21 percent. |
| Author | Ray Jinzhu Chen |
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| Cites_doi | 10.1109/12.76416 10.2307/3214417 10.1109/TC.1982.1675926 10.1137/0145052 10.1109/32.4676 10.1109/12.477243 10.1109/12.16501 10.1109/12.40849 10.1145/65950.65957 10.1109/TC.1983.1676125 10.1137/0144074 10.1109/71.246075 10.1109/71.674321 10.1109/12.2213 10.2307/1427640 10.1109/TSE.1985.231547 10.1109/WSC.1994.717194 |
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| References | kleinrock (bibL082912) 1975 lipsky (bibL082916) 1992 chen (bibL08294) 2000 bibL082910 bibL082922 bibL082923 sholl (bibL082924) 1992 bibL08299 bibL08298 bibL08297 chen (bibL08295) 1991 chen (bibL08293) 1998 bibL08292 bibL08291 bibL082921 bibL082911 lui (bibL082918) 1995; 44 bibL082913 bibL082914 bibL082915 bibL082917 bibL082919 ding (bibL08296) 1990 thomasian (bibL082925) 1994 makowski (bibL082920) 1994 |
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| Snippet | A new analysis technique, dynamic-bubblesort analysis, is introduced for general K-queue first-in-first-out HFJ (homogenous fork/join queuing) systems of K/spl... Task k, k=1, 2, ..., K, is assigned to the kth queuing system, which is a first-in-first-out server with a general service distribution and an infinite... A new analysis technique, dynamic-bubblesort analysis, is introduced for general K-queue first-in-first-out HFJ (homogenous fork/join queuing) systems of K... A new analysis technique, dynamic-bubblesort analysis, is introduced for general K-queue first-in-first-out HFJ (homogenous fork/join queuing) systems of K 2 .... |
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| SubjectTerms | Analytical models Application software Arrivals Computational modeling Computer Society Concurrent computing Delay Mathematical models Parallel processing Performance analysis Queueing analysis Queues Queuing theory Servers Simulation Studies Synchronization Tasks Upper bound Upper bounds |
| Title | A hybrid solution of fork/join synchronization in parallel queues |
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