### Table 1: A comparison of N-process k-exclusion algorithms for shared-memory systems. Time complexity is measured

1997

"... In PAGE 2: ... The renaming algorithm we presentis based on test-and-set, and has time complexity that is directly proportional to the number of processes that concurrently hold or request names. Table1 compares the k-exclusion algorithms presented in this paper to previously known ones. This table gives the time complexity (see below) of each listed algorithm, both under contention and in the absence of contention.... In PAGE 2: ...his usage is consistent with the notion of contention for the implemented object (i.e., the number of processes that concurrently access the object). Table1 also speci es the set of instructions used byeach algorithm, and whether or not the algorithm is starvation-free. Time complexity gures in the table specify the number of remote accesses of shared memory required per critical section acquisition.... In PAGE 3: ... Hence, they can be implemented on distributed shared-memory machines that do not have coherentcaches. For both classes of machines, we present algorithms that have O(k log(N=k)) time complexity under contention and algorithms that have time complexity that is directly proportional to contention (see Table1 ). As shown in Table 1, all of these algorithms have constant time complexity in the absence of contention, and are based on commonly-available synchronization primitives.... ..."

Cited by 12

### Table 1: A comparison of N-process k-exclusion algorithms for shared-memory systems. Time complexity is measured in terms of the number of remote memory references. Therefore, algorithms that do not spin locally have unbounded time complexity. In the rst column of time complexity gures, c is the level of contention. The compare-and-swap- based algorithms of Theorems 11 and Theorem 12 improve upon the algorithms of Theorems 7 and 8 by having lower space complexity.

"... In PAGE 2: ... The renaming algorithm we present is based on test-and-set, and has time complexity that is directly proportional to the number of processes that concurrently hold or request names. Table1 compares the k-exclusion algorithms presented in this paper to previously known ones. This table gives the time complexity (see below) of each listed algorithm, both under contention and in the absence of contention.... In PAGE 2: ...his usage is consistent with the notion of contention for the implemented object (i.e., the number of processes that concurrently access the object). Table1 also speci es the set of instructions used by each algorithm, and whether or not the algorithm is starvation-free. Time complexity gures in the table specify the number of remote accesses of shared memory required per critical section acquisition.... In PAGE 2: ... Hence, they can be implemented on distributed shared-memory machines that do not have coherent caches. For both classes of machines, we present algorithms that have O(k log(N=k)) time complexity under contention and algorithms that have time complexity that is directly proportional to contention (see Table1 ). As shown in Table 1, all of these algorithms have constant time complexity in the absence of contention, and are based on commonly-available 1The k-assignment problem was originally posed by Attiya et al.... ..."

### Table 6. Comparison of the Ring Mutual Exclusion Algorithms with others

2004

"... In PAGE 9: ... We showed that this architecture provides improvements over message complexities of Ricart and Agrawala and Token-based algorithms and also the time required to execute a critical section. A comparison of the two algorithms with their regular counterparts in terms of their message complexities is shown in Table6 . Here we see that it is possi- ble to obtain an order of magnitude of improvement over the classical RA and the Token-Based algorithms using our model at the expense of large response times and increased synchronization delays.... ..."

Cited by 5

### Table 3 Size of the Markovian semantic models of the six mutual exclusion algorithms

2003

"... In PAGE 41: ... The performance measures we are interested in are the mean numbers of accesses per time unit to the critical section and to the shared variables. They are computed on the Markovian semantic model of each al- gorithm; the size of such models in the case of two programs is shown in Table3 . The former performance index represents the throughput of the al- gorithm and has been specified by assigning bonus reward 1 to every action with type exec csi.... ..."

Cited by 6

### Table 3. Lock and unlock cost models.

"... In PAGE 5: ... Starvation-free also uses CAS for unlock, but it has a FA in critical path for lock oper- ation. We note that the models explain the observed costs in Table3 , in terms of timings of primitive operations (Table 1). 5.... In PAGE 6: ... For Starvation-free, throughput drops by 25%. If we refer to cost model in Table3 , compared to 3 operations in 0% case, we have an additional unsuccessful CAS due to contention which results in 4 operations. For Basecase, the throughput increases relative to 0%, because server is able to overlap acknowledgment of unlock and grant messages, which was not possible in 0% case.... ..."

### Table 9.2: Verification of the mutual exclusion protocol

### Table 1. TCTL5. The TCTL-formula that expresses mutual exclusion is

"... In PAGE 11: ... To apply Kronos we have to translate each of the three automata separately into the Kronos-format timed graphs . The resulting timed graphs had the following dimensions given in Table1 . In addition we have to add two small automata to model the environment.... In PAGE 12: ... This makes the description of the system in Fig. 5 acceptably small (see Table1 ). Uppaal can check a system of Timed Automata against reachability properties like (22) only whereas a forward analysis algorithm is used.... ..."

### TABLE I COMPARISON OF VARIOUS QUORUM-BASED GROUP MUTUAL EXCLUSION ALGORITHMS.

### Table 3. Timed reachability analysis of the mutual exclusion algorithm

"... In PAGE 6: ...4ms, respectively. We show the results in Table3 . For example, the second column shows the results for t = 1ms.... ..."