However, Macduff’s forces arrive under the cover of boughs cut from Birnam wood. He awaits confidently as the prophecy foretold his invulnerability. The news of her suicide reaches Macbeth directly before the arrival of the English forces and sends him into an even deeper despair. While Macbeth awaits his opponents, Lady Macbeth is in the process of going mad, unable to wash the blood from her hands. With Malcom, the two raise an army and ride to Scotland to take on Macbeth with the support of the Scottish nobles who fear Macbeth’s tyranny and murderous ways. In fear, Macbeth seizes Macduff’s castle and orders the murder of his wife and children, inciting Macduff to further rage. He returns home and finds that Macduff has fled to England to join Malcom. He cannot be harmed by any man born of woman and he is safe until Birnam Wood comes to Dunsinane Castle. He must beware of Macduff, a chief opponent to Macbeth taking the throne. To ease his fears, he visits the witches again and they offer to him more prophecies. His very presence as the king of Scotland has angered the other nobles and further incites Macbeth’s misgivings and paranoia. The night of his murder, Banquo’s ghost appears to Macbeth and sends him into hysteria, scaring his guests and angering his wife. Successfully killing Banquo, the murderers fail to kill Fleance. Immediately, Macbeth’s misgivings and trust in the prophecies force his hand in the murder of Banquo and his son Fleance as well, afraid that his heirs will seize the throne. All the while, Duncan’s sons flee the country, afraid for their own lives. When the body of Duncan is discovered in the morning, Macbeth quickly kills the “culprits” and assumes the kingship. The two plan to get Duncan’s chamberlains drunk enough that they will not remember the evening and blame them for the murder. Immediately upon returning to his castle, Lady Macbeth is able to convince her husband to take initiative and murder Duncan that very night. Unlike Macbeth, Lady Macbeth is very sure of her husband’s future, desiring the throne and telling him that they must murder Duncan to ensure his ascension. He invites Duncan to dine at his castle that evening and goes ahead to tell his wife of the day’s events. However, when the two come closer to the encampment, they are presented with a messenger from King Duncan who announces that Macbeth has been made the Thane of Cawdor, immediately putting the prophecy into perspective, making Macbeth wonder how he might become king. The two are sufficiently skeptical and continue their journey home. For Banquo, they prophesize that he will beget the line of Scottish Kings, though he will never become king himself. The witches tell Macbeth of how he will become the Thane of Cawdor and then the King of Scotland. Various challenges in the realization of double auction mechanisms in cloud computing along-with the future possibilities are also presented.The play opens with Macbeth and Banquo, two of the Scottish King Duncan’s generals returning from battle when they encounter three witches in the woods. The performance of TMDA, which addresses the interests of both the cloud user and the provider, has been validated through simulation study. TMDA would also encourage researchers to contribute in this emerging area. TMDA is proven to be asymptotically efficient, individual rational, truthful and budget-balanced. As most of the existing works in double auction confines only resource allocation, therefore, a Truthful Multi-Unit Double Auction mechanism (TMDA) is proposed that would help researchers to understand how a truthful double auction mechanism can be designed. A framework for a future cloud market using double auction is also proposed. This work makes a detailed study of the double auction mechanisms and their applicability for the cloud markets. These models apply economy based approaches e.g. Accordingly, market based resource allocation models for cloud computing have been proposed. This demands efficient allocation of resources to benefit both the cloud users and the cloud service providers. The cloud system is designed, implemented and conceptualized as a marketplace where resources are traded.
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