Pub Date : 2022-07-03DOI: 10.1080/23799927.2022.2113745
Andrew Bowling, Ping Zhang
A zonal labelling of a plane graph G is an assignment of the two nonzero elements of the ring of integers modulo 3 to the vertices of G such that the sum of the labels of the vertices on the boundary of each region of G is the zero element of . A plane graph possessing such a labelling is a zonal graph. A cubic map is a connected 3-regular bridgeless plane graph. It is known that if an independent proof could be given that every cubic map is zonal, then the Four Color Theorem would follow as a corollary. As a step in this direction, it is shown that certain subgraphs of cubic maps are nearly zonal.
{"title":"Inner zonality in graphs","authors":"Andrew Bowling, Ping Zhang","doi":"10.1080/23799927.2022.2113745","DOIUrl":"https://doi.org/10.1080/23799927.2022.2113745","url":null,"abstract":"A zonal labelling of a plane graph G is an assignment of the two nonzero elements of the ring of integers modulo 3 to the vertices of G such that the sum of the labels of the vertices on the boundary of each region of G is the zero element of . A plane graph possessing such a labelling is a zonal graph. A cubic map is a connected 3-regular bridgeless plane graph. It is known that if an independent proof could be given that every cubic map is zonal, then the Four Color Theorem would follow as a corollary. As a step in this direction, it is shown that certain subgraphs of cubic maps are nearly zonal.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82411499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-03DOI: 10.1080/23799927.2022.2096119
G. Tamrakar, Adrish Banerjee, U. C. Gupta
ABSTRACT The present article analyses an infinite buffer batch size-dependent bulk service queue with multiple working vacation (MWV). The customer's arrival pattern follows the Poisson process, and they get the service in batches according to the general bulk service (GBS) rule in regular period (RP) as well as in working vacation period (WVP). After one service in RP, if the queue size is greater or equal to the lower threshold of the GBS rule, then the server performs the service in RP, otherwise, it starts the working vacation (WV) following exponential vacation time distribution. During the WVP, the server serves the customers in batches (if any) at a lower service rate than the usual service rate. The service time in the RP as well as in WVP is generally distributed. At an arbitrary epoch, the joint probabilities of the queue size and batch size with the server in RP as well as in WVP have been obtained using the supplementary variable technique (SVT) and the bivariate generating function method. Finally, some numerical observations are presented to enhance the applicability of the analytical results.
{"title":"Analysis of batch size-dependent bulk service queue with multiple working vacation","authors":"G. Tamrakar, Adrish Banerjee, U. C. Gupta","doi":"10.1080/23799927.2022.2096119","DOIUrl":"https://doi.org/10.1080/23799927.2022.2096119","url":null,"abstract":"ABSTRACT The present article analyses an infinite buffer batch size-dependent bulk service queue with multiple working vacation (MWV). The customer's arrival pattern follows the Poisson process, and they get the service in batches according to the general bulk service (GBS) rule in regular period (RP) as well as in working vacation period (WVP). After one service in RP, if the queue size is greater or equal to the lower threshold of the GBS rule, then the server performs the service in RP, otherwise, it starts the working vacation (WV) following exponential vacation time distribution. During the WVP, the server serves the customers in batches (if any) at a lower service rate than the usual service rate. The service time in the RP as well as in WVP is generally distributed. At an arbitrary epoch, the joint probabilities of the queue size and batch size with the server in RP as well as in WVP have been obtained using the supplementary variable technique (SVT) and the bivariate generating function method. Finally, some numerical observations are presented to enhance the applicability of the analytical results.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81609874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-03DOI: 10.1080/23799927.2022.2071765
K. Ganesamoorthy, M. Murugan, A. Santhakumaran
For a connected graph G of order at least two, a connected monophonic set of G is a monophonic set S such that the subgraph induced by S is connected. The minimum cardinality of a connected monophonic set of G is the connected monophonic number of G and is denoted by . The number of extreme vertices and cut-vertices of G is its extreme-cut order . A graph G is an extreme-cut connected monophonic graph if . Some interesting results on the extreme-cut connected monophonic graphs G are studied. For positive integers r, d and with r
{"title":"On the connected monophonic number of a graph","authors":"K. Ganesamoorthy, M. Murugan, A. Santhakumaran","doi":"10.1080/23799927.2022.2071765","DOIUrl":"https://doi.org/10.1080/23799927.2022.2071765","url":null,"abstract":"For a connected graph G of order at least two, a connected monophonic set of G is a monophonic set S such that the subgraph induced by S is connected. The minimum cardinality of a connected monophonic set of G is the connected monophonic number of G and is denoted by . The number of extreme vertices and cut-vertices of G is its extreme-cut order . A graph G is an extreme-cut connected monophonic graph if . Some interesting results on the extreme-cut connected monophonic graphs G are studied. For positive integers r, d and with r<d, there exists an extreme-cut connected monophonic graph G with monophonic radius r, monophonic diameter d and the connected monophonic number k. Also if p, d and k are positive integers such that and , then there exists an extreme-cut connected monophonic graph G of order p with monophonic diameter d and .","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73089915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-03DOI: 10.1080/23799927.2022.2072400
Leila Saadi, Badreddine Benreguia, C. Arar, Moumen Hamouma
This paper deals with the problem of finding dominating set using self-stabilization paradigm in distributed systems. Usually, members of a dominating set are selected to be as cluster heads in Wireless Sensor Networks (WSN) to ensure a permanent service availability. Since failures occur frequently inside WSN due to limited battery energy, self-stabilizing algorithm allows recomputing the dominating set, and hence the network returns to its ordinary running. Existing works have introduced many variants of self-stabilizing algorithms that compute minimal dominating set S where each node out of S has neighbours in S more than it has out S. In this paper, we introduce a generalized self-stabilizing algorithm called minimal -dominating set. An α-dominating set is a subset of nodes S such that for any node v out of S, the rate of neighbours of v inside S must be greater than α, where . In the same way, an -dominating set is a subset of nodes S such that: S is α-dominating set and for each node v in S, the rate of neighbours of v inside S is greater than β, where . Mathematical proofs and simulation tests show the correctness and the efficiency of the proposed algorithm. Through our proposed variant -domination, we prove rigorously the conjecture of Carrier et al. [Self-stabilizing (f,g)-alliances with safe convergence, J. Parallel Distrib. Comput. 81–82 (2015), pp. 11–23. doi:10.1016/j.jpdc.2015.02.001] who have proposed a self-stabilizing algorithm for a domination variant called -alliance set only when . We prove the correctness of the case f
{"title":"Self-stabilizing algorithm for minimal (α,β)-dominating set","authors":"Leila Saadi, Badreddine Benreguia, C. Arar, Moumen Hamouma","doi":"10.1080/23799927.2022.2072400","DOIUrl":"https://doi.org/10.1080/23799927.2022.2072400","url":null,"abstract":"This paper deals with the problem of finding dominating set using self-stabilization paradigm in distributed systems. Usually, members of a dominating set are selected to be as cluster heads in Wireless Sensor Networks (WSN) to ensure a permanent service availability. Since failures occur frequently inside WSN due to limited battery energy, self-stabilizing algorithm allows recomputing the dominating set, and hence the network returns to its ordinary running. Existing works have introduced many variants of self-stabilizing algorithms that compute minimal dominating set S where each node out of S has neighbours in S more than it has out S. In this paper, we introduce a generalized self-stabilizing algorithm called minimal -dominating set. An α-dominating set is a subset of nodes S such that for any node v out of S, the rate of neighbours of v inside S must be greater than α, where . In the same way, an -dominating set is a subset of nodes S such that: S is α-dominating set and for each node v in S, the rate of neighbours of v inside S is greater than β, where . Mathematical proofs and simulation tests show the correctness and the efficiency of the proposed algorithm. Through our proposed variant -domination, we prove rigorously the conjecture of Carrier et al. [Self-stabilizing (f,g)-alliances with safe convergence, J. Parallel Distrib. Comput. 81–82 (2015), pp. 11–23. doi:10.1016/j.jpdc.2015.02.001] who have proposed a self-stabilizing algorithm for a domination variant called -alliance set only when . We prove the correctness of the case f","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75003582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-31DOI: 10.1080/23799927.2022.2059012
Sahil Sharma, V. K. Bhat
Let be a simple, connected, and undirected graph. The distance between two vertices denoted by , is the length of the shortest path connecting u and v. A subset of vertices is said to be a resolving set for G if for any two distinct vertices V, there exist a vertex such that . A minimal resolving set is called a metric basis, and the cardinality of the basis set is called the metric dimension of G, denoted by . In this article, we find the metric dimension for two infinite families of plane graphs and , where is obtained by the combination of copies of bipartite graphs , and is obtained by the combination of double antiprism graph with antiprism graph and then adding n-paths of length p.
{"title":"Vertex resolvability of convex polytopes with n-paths of length p","authors":"Sahil Sharma, V. K. Bhat","doi":"10.1080/23799927.2022.2059012","DOIUrl":"https://doi.org/10.1080/23799927.2022.2059012","url":null,"abstract":"Let be a simple, connected, and undirected graph. The distance between two vertices denoted by , is the length of the shortest path connecting u and v. A subset of vertices is said to be a resolving set for G if for any two distinct vertices V, there exist a vertex such that . A minimal resolving set is called a metric basis, and the cardinality of the basis set is called the metric dimension of G, denoted by . In this article, we find the metric dimension for two infinite families of plane graphs and , where is obtained by the combination of copies of bipartite graphs , and is obtained by the combination of double antiprism graph with antiprism graph and then adding n-paths of length p.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81533919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-18DOI: 10.1080/23799927.2023.2166872
T. Yamakami
The closure of deterministic context-free languages under logarithmic-space many-one reductions ( -m-reductions), known as LOGDCFL, has been studied in depth from an aspect of parallel computability because it is nicely situated between and . By replacing a memory device of pushdown automata with an access-controlled storage tape, we introduce a computational model of one-way deterministic depth-k storage automata (k-sda's) whose tape cells are freely modified during the first k accesses and then become blank forever. These k-sda's naturally induce the language family . Similarly to , we study the closure of all languages in under -m-reductions. We demonstrate that by significantly extending Cook's early result (1979) of . The entire hierarch of for all therefore lies between and . As an immediate consequence, we obtain the same simulation bounds for Hibbard's limited automata. We further characterize in terms of a new machine model, called logarithmic-space deterministic auxiliary depth-k storage automata that run in polynomial time. These machines are as powerful as a polynomial-time two-way multi-head deterministic depth-k storage automata. We also provide a ‘generic’ -complete language under -m-reductions by constructing a two-way universal simulator working for all k-sda's.
{"title":"Between SC and LOGDCFL: families of languages accepted by logarithmic-space deterministic auxiliary depth-k storage automata","authors":"T. Yamakami","doi":"10.1080/23799927.2023.2166872","DOIUrl":"https://doi.org/10.1080/23799927.2023.2166872","url":null,"abstract":"The closure of deterministic context-free languages under logarithmic-space many-one reductions ( -m-reductions), known as LOGDCFL, has been studied in depth from an aspect of parallel computability because it is nicely situated between and . By replacing a memory device of pushdown automata with an access-controlled storage tape, we introduce a computational model of one-way deterministic depth-k storage automata (k-sda's) whose tape cells are freely modified during the first k accesses and then become blank forever. These k-sda's naturally induce the language family . Similarly to , we study the closure of all languages in under -m-reductions. We demonstrate that by significantly extending Cook's early result (1979) of . The entire hierarch of for all therefore lies between and . As an immediate consequence, we obtain the same simulation bounds for Hibbard's limited automata. We further characterize in terms of a new machine model, called logarithmic-space deterministic auxiliary depth-k storage automata that run in polynomial time. These machines are as powerful as a polynomial-time two-way multi-head deterministic depth-k storage automata. We also provide a ‘generic’ -complete language under -m-reductions by constructing a two-way universal simulator working for all k-sda's.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81200948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-01DOI: 10.1080/23799927.2022.2048206
Alessandro Barenghi, Jean-François Biasse, Tra Ngô, Edoardo Persichetti, P. Santini
The LESS signature scheme, introduced in 2020, represented a fresh start for code-based signatures. In this paper we explore advanced functionalities for signature schemes, stemming from the work of LESS. First, we adapt a recent protocol of Beullens et al. to obtain a construction for (linkable) ring signatures. Then, we realize an identity-based signature scheme following the traditional approach by Joye and Neven. Our performance numbers confirm that signature schemes based on the code equivalence problem have considerable potential for practical applications.
{"title":"Advanced signature functionalities from the code equivalence problem","authors":"Alessandro Barenghi, Jean-François Biasse, Tra Ngô, Edoardo Persichetti, P. Santini","doi":"10.1080/23799927.2022.2048206","DOIUrl":"https://doi.org/10.1080/23799927.2022.2048206","url":null,"abstract":"The LESS signature scheme, introduced in 2020, represented a fresh start for code-based signatures. In this paper we explore advanced functionalities for signature schemes, stemming from the work of LESS. First, we adapt a recent protocol of Beullens et al. to obtain a construction for (linkable) ring signatures. Then, we realize an identity-based signature scheme following the traditional approach by Joye and Neven. Our performance numbers confirm that signature schemes based on the code equivalence problem have considerable potential for practical applications.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83574921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-12-09DOI: 10.1080/23799927.2021.2014977
Peter Broe, G. Chartrand, Ping Zhang
For a non-negative integer r, the r-orbit of a vertex v in a connected graph G of order n is the set of vertices at distance r from v. A sequence of positive integers with is called an irregular orbital dominating sequence of G if for every pair i, j of integers with and G contains distinct vertices such that We investigate graphs that possess and graphs do not possess an irregular orbital dominating sequence. It is shown that a non-trivial tree has an irregular orbital dominating sequence if and only if it is neither a star, a path of order 2, nor a path of order 6.
{"title":"Irregular orbital domination in graphs","authors":"Peter Broe, G. Chartrand, Ping Zhang","doi":"10.1080/23799927.2021.2014977","DOIUrl":"https://doi.org/10.1080/23799927.2021.2014977","url":null,"abstract":"For a non-negative integer r, the r-orbit of a vertex v in a connected graph G of order n is the set of vertices at distance r from v. A sequence of positive integers with is called an irregular orbital dominating sequence of G if for every pair i, j of integers with and G contains distinct vertices such that We investigate graphs that possess and graphs do not possess an irregular orbital dominating sequence. It is shown that a non-trivial tree has an irregular orbital dominating sequence if and only if it is neither a star, a path of order 2, nor a path of order 6.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86541866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-05DOI: 10.1080/23799927.2021.1983876
Elham Abdali, K. Moradipour, Sanaz Asadi-Rahmati, Maryam Fallah
In the network DEA models, it is assumed that all inputs are varied according to decisions of manager. However, in many cases, there are non-discretionary inputs that are beyond the control of a sub-DMUs and DMUs management in the efficiency evaluation, and this problem has not been discussed considerably in network DEA so far. This study proposed a multiplier model to treat a two-stage network system comprised of three sub-DMUs in hybrid form with non- discretionary inputs and shared discretionary inputs, while this issue is not sufficiently rich in the network systems, here, it is being analysed seriously in this study. The proposed model simulate precisely the parallel-series internal structure of network system with non-discretionary inputs and shared discretionary inputs between sub-DMUs, and also uses synthetically additive and multiplicative DEA approaches for evaluating the efficiency of two-stage network system. Finally, a practical example demonstrates the feasibility of the proposed model.
{"title":"Efficiency evaluation in hybrid two-stage network DEA with non-discretionary inputs and shared discretionary inputs","authors":"Elham Abdali, K. Moradipour, Sanaz Asadi-Rahmati, Maryam Fallah","doi":"10.1080/23799927.2021.1983876","DOIUrl":"https://doi.org/10.1080/23799927.2021.1983876","url":null,"abstract":"In the network DEA models, it is assumed that all inputs are varied according to decisions of manager. However, in many cases, there are non-discretionary inputs that are beyond the control of a sub-DMUs and DMUs management in the efficiency evaluation, and this problem has not been discussed considerably in network DEA so far. This study proposed a multiplier model to treat a two-stage network system comprised of three sub-DMUs in hybrid form with non- discretionary inputs and shared discretionary inputs, while this issue is not sufficiently rich in the network systems, here, it is being analysed seriously in this study. The proposed model simulate precisely the parallel-series internal structure of network system with non-discretionary inputs and shared discretionary inputs between sub-DMUs, and also uses synthetically additive and multiplicative DEA approaches for evaluating the efficiency of two-stage network system. Finally, a practical example demonstrates the feasibility of the proposed model.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75898846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-30DOI: 10.1080/23799927.2021.2000503
Gagandeep Singh, A. Kumari, U. C. Gupta
In this paper, we consider a single server bulk service queue, with modified bulk service rule, say rule, wherein customers are served in batches of maximum batch size K with minimum threshold value L. Further, we allow the customers to enter the service if the server has begun the service and is having less than K customers. In addition, service rates of the batches are taken to be dependent on the size of the batch. Analytic expressions for the joint probability distribution of the number of customers in the queue, and with the server, the marginal probability distribution of the number of customers in the queue, system and with the server is derived. A thorough numerical investigation of the effect of various parameters on the distributions obtained above is done and numerical results are presented in the form of tables and graphs. We also obtain various performance measures (both in closed-form as well as numerically) such as the average number of customers in the queue, system, with the server, etc.
{"title":"Stationary system-length distribution of Markovian bulk service queue with modified bulk service rule and dynamic service rates","authors":"Gagandeep Singh, A. Kumari, U. C. Gupta","doi":"10.1080/23799927.2021.2000503","DOIUrl":"https://doi.org/10.1080/23799927.2021.2000503","url":null,"abstract":"In this paper, we consider a single server bulk service queue, with modified bulk service rule, say rule, wherein customers are served in batches of maximum batch size K with minimum threshold value L. Further, we allow the customers to enter the service if the server has begun the service and is having less than K customers. In addition, service rates of the batches are taken to be dependent on the size of the batch. Analytic expressions for the joint probability distribution of the number of customers in the queue, and with the server, the marginal probability distribution of the number of customers in the queue, system and with the server is derived. A thorough numerical investigation of the effect of various parameters on the distributions obtained above is done and numerical results are presented in the form of tables and graphs. We also obtain various performance measures (both in closed-form as well as numerically) such as the average number of customers in the queue, system, with the server, etc.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73330484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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