INTRODUCTION:

Cloud computing has been accredited with the growing effectiveness through cost saving, better flexibility, elasticity and best resource utilization. Cloud computing is also considered as infrastructure service to clients on a remote basis over the internet. A suitable managing of resources in the clouds is critical for effectually joining the power of the underlying dispersed resources and infrastructure. The difficulties range from handling resource heterogeneity, allocating resources to user requests efficiently as well as effectively scheduling the requests that are mapped to given resource, as well as handling reservations associated with the workload and the system. As a consumer or user of cloud, one should be aware of the ways and means with which the cloud resources are allocated to user requirements, and how are the applications being executed in a cloud environment.

Queueing theory is based on mathematical learning of queues or else waiting lines. The queue is designed when the request for service surpasses the capacity to deliver service at that point in time. A traditional queueing system may be defined as one having a service facility, at which customers arrive for service and when there are additional clients in the system than the service facility can handle instantaneously, a queue or waiting line is established. The waiting customers take their turn for service according to a pre-assigned rule and leave the system after availing service. Thus, the input to the system consists of the customers demanding service and the output refers to the served customers. Hence, we have model the cloud center as serially connected M ^[x]/M/1and M/M/1queueing system which designates that customers are arriving in batches or groups with Poisson arrivals and service are done by exponentially distributed. Thus, we have analysed performance measures such as total number of users / clients waiting for service in both queues and the total number of users / clients in the system for arbitrary batch size and for constant batch size. Finally, the total waiting time of different class i of users /clients versus service rate of the system and the total waiting time of different class i of users / clients versus different batch sizes have been shown graphically.

RELATED WORKS:

Cloud computing is based on distribution of computing services done by the Internet. Cloud services license individuals and trades to usage of software and hardware that are accomplished by third parties at remote locations. For example, cloud services contain community networking sites, web mail, online file storage and online business applications. Cloud computing delivers a shared pool of resources, including networks, computer processing power, data storage space and specialized corporate and user applications.[1]. Khazaei [2] have described about model which permits cloud operators to define the connection between the amount of servers and input buffer size and also consider the performance indicators such as average number of tasks in the system, probability that a job will attain immediate service and also blocking probability. Anupama [3] have described about to analyse the dynamic presentation of infinite severs in excess of single server. They also considered the length of service, utilization factor, throughput, waiting time of infinite server system. Muthu [4] have described about logical technique based on an estimated Markov chain model for performance assessment of a cloud computing center, the nature of the cloud environment to expected overall service time for requests for the huge amount of servers, which marks model flexible in terms of scalability and variety of service time.

Aattar et al., [5] have described a finite capacity(buffer) multiple server queueing model for designing cloud data center with GE distribution task arrivals and general service time distribution for requests. Using this model, they have obtained the performance analysis of cloud server frames, an accurate estimate of the whole probability distribution of the request response time and additional important performance pointers such as the mean number of tasks in the system, the distribution of waiting time, blocking probability and the probability of immediate service.

Mary et al., [6] have described an analytical model for show assessment of a cloud computing data centre. Using simulation, mean and standard deviation can be computed, the blocking probability and also probability of immediate service can be computed, Varma et al., [7] have developed and analysed cloud computing model by applying queueing theory to distribute resources dependent upon buffer size, which can development the performance of cloud. It also comparatively reduces the queue length and mean delay, which exposed marvellous effect on performance measures similar throughput, utilization and mean delay. Bai et al., [8] have considered a complex queueing model in order to assess the performance of heterogeneous cloud data centers. They also analysed average response time, waiting time and other significant performance indicators. Finally this queueing model delivers results with a high degree of accuracy for each performance metric and allows for a sophisticated study of heterogeneous cloud data centers. Marcu et al., [9] considered the model M/M/s and M/M/1 queue in series in which different priority clients / patients / users obtained service from the first queue and enter into the second queue to get service from the server with probability p or directly access the database with probability (1– p). Furthermore, the authors have considered an e-health solution based on healthcare information systems combination and cloud computing idea with a focus on medical imaging department. They also considered Hybrid cloud architecture and request management application which have been analysed in terms of waiting time well-defined as Quality of Service criteria (QoS). Furthermore, they have obtained waiting time of a class of units or patients in both M/M/s queue and M/M/1 queue and total waiting time for this model.

PROPOSED WORK:

In this paper, we consider two types of queueing model M^[x]/M/1 and M/M/1 in series for designing cloud infrastructure for healthcare system in which multiple priority batches (bulk) of clients / users from the public cloud enter into the system for service using FCFS discipline. If server is free then it gets the service (access data from the cloud data base) and leaves the system. Otherwise it is to be stayed in queue until get the server. The batch of different priority class iusers / patients / clients request for service in the cloud environment. We consider arrivals are different class i each of which follows a Poisson distribution with rate λ_i (i = 1, 2…n) and single server provide service to each class i. The service time of each class follows an exponential distribution with rate μ_i. After completing service from M^[x]/M/1 queue each class ienters into M/M/1queue for service for accessing cloud database with probability ϕ. Otherwise, users / clients leave the system with probability (1- ϕ) without entering the second queue. In this paper, we use queueing models for cloud computing architecture which is applied in healthcare centres. After completed service (primary service such as appointment, consultation, physical test etc., ) from M^[X]/M/1 queue usually, clients / patients / users request medical staff for accessing database from the cloud if the medical staff (server) is free. Otherwise, clients / users will wait in the queue until its turn to come or they may leave the system with probability (1- ϕ).

Table 1. Nomenclature

Notation	Meaning
λ_i	Arrival rate, i=1, 2, …n
µ_i	Service rate, i= 1, 2…n
ϕ	Probability that units enter into the second queue
ρ	Utilization factor
ρ₁	M^[X]/M/1 Utilization factor
ρ₂	M/M/1Utilization factor
π₀	Probability that the server is idle (free)
ℓ	Constant batch size
	The average waiting time of units in the first queue
W _M/M/1	The average waiting time of units in the second queue
W_TQWT	Expected Total Queue Waiting Time
W_TSWT	Expected System Waiting Time

According to Kendall notation for queues, we study the model of a cloud system collected by two serially connected queues M^[X]/M/1 entry queue and M/M/1 classical queue. We use the above notations for describing system. For this model, we obtain waiting time of each class in classical batch arrival queue as well as in classical single server queue for the case 0 ≤ ϕ ≤ 1. The system is stable if

(1)

Where and

Since the arrival stream to entry queue follow a Poisson distribution, the random variable X denotes the number of clients / users arriving for service, with probability b_n, n > 0. Clearly, b _n = λ _n/ λ,

Where λ _n- the arrival rate of batches of size n,

λ₌, the composite arrival rate of all batches.

For an arbitrary batch-size distribution X, we first define the following probability and batch size generating functions in steady state

(2)

Using above definition, we obtain the following equation,

(3)

On simplifying, we have

(4)

Since, we have (5)

Differentiate (4) with respect to z, we have

(6)

We obtain performance measures of the cloud system in two different cases.

Case I: If the batch size is arbitrary, we obtain the following performance measures:

(i) The average number of clients / users in the system, (7)

(ii) The average number of a client / user wait in the system, (8)

(iii) The average number of clients / users in the system, (9)

(iv) The average number of a client / user wait in the queue, (10)

Case II: If the batch size is, a constant, we obtain the following performance measures:

(v) The average number of clients / users in the system, (11)

(vi)The average numbers of a client / user wait in the system, (12)

(vii)The average number of clients / users in the queue, (13)

(viii)The average numbers of a client / user wait in the queue, (14)

Suppose that after completing service from the entry queue called bulk input queue, the i^th priority clients / users arriveon a first-come, first-served basis according to a Poisson process with rate at an M/M/1 queue and the service time distribution of i^th priority client / user follow exponential distribution with mean.We define the following in steady state.

(15)

If S_q is the waiting timeof new k^thpriority clients / users (k <i), then

(16)

Where - the time required to serve thenumber of clients / users of priority k who enter and go ahead of the entering clients / users ( k <i).

T_k-the time required to serve the number of clients / users of priority k already in the queue ahead of the entering customer ( ).

T₀- the time required to complete service of the clients / users who already in service (note that T₀= 0

when the system is empty upon arrival).

(17)

Where , and

On simplifying equation (17) by using above equation, we get

The mean waiting time of i^th priority clients / users in the queue is (18)

The mean waiting time of overall clients / users in the queue is (19)

Thus,

(i)The total waiting time of a client / user wait in both the queues is (20)

(ii)The total waiting time of a client/ user wait in both the queues is(21)

NUMERICAL RESULTS:

The simulation of the queueing system is done using SHARPE tool. The performance evaluation of the proposed model bulk input M^[X]/M/1 and M/M/1in series is analysed for a particular situation based on numerical results in this section. The simulation of this kind is analysed to visualise the Quality of Service metrics such as utilisation of the server of the system and waiting time. We assume that arrival rate of the request in the system λ₁=5requests (high level priority), λ₂= 2λ₁ requests(medium level priority) and λ₃= 3λ₁ requests (low level priority) for class1, class2 and class3 priority units respectively and service time μ = 100, …, 160 to each class of users for M^[X]/M/1 queue and μ = 160 to all class of users for M/M/1 queue with probability = 0.5 for all class of patients/clients. Fig (2) shows that as the service rate increases gradually, the total waiting time of queues, W_TQWT and the total waiting of the system, W_TSWT decreases gradually. Moreover, we observe that the considerable variation in the total waiting time between high level priority (class 1) units and high level priority (class 1) units whereas the total waiting time W_TQWTof medium level priority (class 2) is smaller than the total waiting time W_TSWTof medium level priority (class 2). Also, the total waiting time, W_TSWTof low level priority (class 3) units is higher than the total waiting time W_TQWTof low level priority (class 3) units. So, comparatively the total waiting time of the queues, W_TQWTis considerably lower than the total waiting time of the system, W_TSWT.

We observe that as the batch size ()increases gradually, the waiting time of both queues and the system increases gradually from Fig (3). Furthermore, there is no much more difference between high level priority class1 units in both queues and the system. But, the increase in total waiting time of medium level priority class 2 units of the system for the probability ϕ = 0.5 is smaller than the total waiting time of medium level priority class 2 units of the queue and the similar observation happened between the low level priority class 3 units in both queues and the system for the probability ϕ = 0.5 due to the fixed service rate = 160.

Fig.2: Service rate Vs Total waiting time

Fig.3: Batch Size ℓ Vs Total Waiting Time

CONCLUSION:

We have proposed the model for cloud computing architecture to analyse performance measure such as waiting time of different class i of units from the public cloud who access cloud database. We simulated our proposed model using SHARPE tool. The results analysed by proposed model shows enhancement in the performance of the cloud queueing system. The performance of the cloud system is measured by using the total waiting time and utilisation of resources. Simulation results showed that the significant variation between the total waiting time and the total number of users / clients in the system for different service rates and for different batch sizes. We are also going to study the above model for the general service time distribution and server’s vacation for our future work.

REFERENCE:

1. Vaquero LM, Merino RL, Caceres J and Lindner M. A break in the clouds: Towards a cloud definition. ACM SIGCOMM Computer Communication Review. 2009; 39 (1): 50–55.

2. Khazaei H. Performance Analysis of Cloud Computing Centers Using M/G/m/m+ r Queuing Systems. IEEE Transactions on Parallel and Distributed Systems. 2012; 23(5):1-10

3. Anupama A. Using Queuing theory the performance measures of cloud with infinite servers. International Journal of Computer Science and Engineering Technology (IJCSET) 2014; 5(1)

4. Muthu A. Performance Analysis of Cloud Computing Centers using M/G/m/m+ r Queuing Systems. International Journal of Research in engineering, science and technologies.2016; 2(2).

5. Aattar MB. Performance Modeling for a Cloud Computing Center Using GE/G/m/k Queuing System International Journal of Science and Research (IJSR). 2014; 3 (5).

6. Mary AR and Saravanan K. Performance Factors of Cloud Computing Data Centers Using [(M/G/1):(∞/GDModel)] Queuing Systems International Journal of Grid Computing and Applications (IJGCA). 2013; 4(1): 1-10

7. Varma P, Suresh A, Satyanarayana and Sundari RMV. Performance analysis of cloud computing using queuing models. Cloud Computing Technologies, Applications and Management (ICCCTAM). 2012 International Conference on. IEEE.

8. Ben M and Haqiq A. Performance Modeling for a Cloud Computing Center Using GE/G/m/k Queuing System. International Journal of Science and Research (IJSR), 2014; 3(5):1-10.

9. Marcu R, Popescu D and Danila J. Healthcare Integration Based on Cloud Computing. U.P.B. Sci. Bull. 2015; 77(2): 31-42.

10. John N and Shenoy S. Health Cloud - Healthcare As service (HaaS) In: Proc. of International Conf. on Advances in Computing. Communications and Informatics (ICACCI). 2014; 1963-1966.

11. Khazaei H, Misic J and MisicVB. Performance Analysis of Cloud Computing Centers using M/G/m/m+r Queuing System. IEEE transactions on parallel and distributed systems.2012; 23(5):936-943.

12. Xiong and Perros H. Service performance and analysis in cloud computing. IEEE Computer Society 2009; 693–700.

13. SorinaLupşe O, Marcella M Vida and Stoicu-Tivadar L. Cloud Computing and Interoperability in Healthcare Information System. The First International Conference on Intelligent Systems and Applications. 2012; 81-85.

14. Umamakeswari A, Vijalakshmi N and Renuga devi T. Storage and Retrieval of medical images using cloud computing Journal of Artificial Intelligence. 2012; 5(4): 207-213.

15. MaN, Mark J. Approximation of the mean queue length of an M/G/c queueing system. Oper Res, 1998; 43:158–165.

16. Gross. D, Harris. C, Fundamental of queueing theory, John Wiley and Sons, Fourth edition. 2014.

17. Santhi K, Saravanan R. A survey on queueing models for cloud computing International Journal of Pharmacy and Technology 2016; 8(2): 3964-3977.

18. Kleinrock. L. Queueing Systems: Theory. Vol.1. A Wiley- Interscience, New York. 1975.

19. Trivedi KS and Sahner R. SHARPE at the age of twenty two ACM SIGMETRICS Performance Evaluation Review. 2009; 36(4): 52-57.

20. Agrawal P, Rathore Y. An Approach for Effective Resource Management in Cloud Computing. Int. J. Tech.2011; 1(2): 121-124.

21. Baghel S.K, Dewangan. B.K. Defense in Depth for Data Storage in Cloud Computing. Int. J. Tech. 2012; 2(2): 58-61.

22. Anjaneyulu GSGN, Sisodiya Y.S, Saurav.K. Novel Composite Encryption for Secrecy in Cloud Computing. Research J. Pharm. and Tech 2016; 9(9):1501-1504.

23. Sunil K. Bedi. Security Measures to Protect Sensitive Customer Data in Cloud Computing. Asian J. Management; 2017; 8(1):12-18.

24. Manu A.P, Shishodia. A, Patle. V.K, Vyas. O.P. State of the Art of Cloud Computing and its Research Issues. Research J. Science and Tech. 2010; 2(6): 117-128.

25. Nadekar. K.G, Ramteke S.H, Babulkar P.S, Jotesh R. Aote D.N. Annexure Privacy Preserving Public Auditing for Data Storage Security in Cloud Computing. Research J. Engineering and Tech. 2015; 6(2): 301-304.

26. Leeladhar A, Prabadevi B. Enhanced ID-Based Ring Signature by Validating Time Slots in Cloud Environment. Research J. Pharm. and Tech. 2017; 10(1): 65-69.

27. Surya V, Albert Mayan J. A Secure Data Sharing Mechanism In Dynamic Cloud By Using KP-ABE. Research J. Pharm. and Tech. 2017; 10(1): 83-86.

28. Vijay P, Sakthivel R. Consumers buying Preference of Mobile Network Service Providers with Special Reference to Salem City, Tamil Nadu. Asian J. Management. 2012; 3(3): 158-162.

29. Thakur A, Yadav KK, Lamba B. eWOM in Social Networking Sites: An Empirical Study of Youth Purchase Behavior towards Laptop. Asian J. Management 2013; 4(4): 12-316.

30. Patle VK. Spatial-Temporal Data Mining in Wireless Sensor Networks. Research J. Science and Tech.2014; 6(2): 87-90.

31. Santhi K, Saravanan R. Performance Analysis of Cloud Computing in Healthcare System Using Tandem Queues. International Journal of Intelligent Engineering and Systems 2017; 10(4): 256-264.

Received on 30.06.2017 Modified on 20.07.2017

Research J. Pharm. and Tech 2017; 10(10):3331-3336.

DOI: 10.5958/0974-360X.2017.00591.1