A stochastic analysis of goods allocation by queuing and the prevention of violence

Batabyal, Amitrajeet and Herath, Gamini (2010): A stochastic analysis of goods allocation by queuing and the prevention of violence. Published in: Economics Bulletin , Vol. 30, (27 November 2010): pp. 3141-3151.

Abstract

When demand for a good exceeds its supply, queuing mechanisms are commonly used to allocate the good in question to citizens. However, very long queues result in excessive wait times and this can lead to violence. As such, the purpose of this paper is to analyze two stochastic models of goods allocation with queuing and the possibility of violence. In the first model, there is no capacity constraint. Using this model, we compute the long run delay per citizen in allocating the pertinent good. Next, we discuss the computation of the equilibrium probabilities for our discrete-time Markov chain theoretic model. In the second model, we capture the violence aspect of the underlying story explicitly with a capacity constraint. Then, we compute the long run fraction of citizens who are not provided the relevant good and the long run fraction of time the good allocating public official is busy.

• Item Type: MPRA Paper
• Language: English
• Keywords: Capacity Constraint, Goods Allocation, Queuing Mechanism, Scarcity, Violence
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; H - Public Economics > H4 - Publicly Provided Goods > H40 - General; O - Economic Development, Innovation, Technological Change, and Growth > O1 - Economic Development > O12 - Microeconomic Analyses of Economic Development

References

Anonymous. (2003) “Pyrrhus of Caracas” The Economist, January 2.

Anonymous. (2008) “Will the dam burst?” The Economist, September 11.

Anonymous. (2009) “Oblivious to the coming storm” The Economist, February 9.

Athreya, K.B. and M. Majumdar (2005) “A note on closing the windows: Some lessons from queuing theory” International Journal of Economic Theory 1, 73-81.

Batabyal, A.A. (2005a) “On the allocation of commodities by queuing and the prevention of violence” Economics Bulletin 15, 1-7.

Batabyal, A.A. (2005b) “On bribing and balking in a simple queuing model of resource allocation” Economics Bulletin 16, 1-10.

Batabyal, A.A. and P. Nijkamp (2004) “Favoritism in the public provision of goods in developing countries” Economics Bulletin 15, 1-10.

Batabyal, A.A. and S.J. Yoo (2007) “Corruption, bribery, and wait times in the public allocation of goods in developing countries” Review of Development Economics 11, 507-17.

Gunawardana, P.J. (2000) “Concessional sales, open market demand, and the consumption of rice in Sri Lanka” International Journal of Social Economics 27, 847-61.

Lui, F.T. (1985) “An equilibrium queuing model of bribery” Journal of Political Economy 93, 760-81.

Pisani, M.J. and J.A. Pagan (2003) “Sectoral queuing in a transitional economy: The case of Nicaragua in the 1990s” Labour 17, 571-97.

Ross, S.M. (2003) Introduction to Probability Models, 8th edition, Academic Press: San Diego, California.

Serneels, P. (2007) “The nature of unemployment among young males in urban Ethiopia” Review of Development Economics 11, 170-86.

Tijms, H.C. (2003) A First Course in Stochastic Models. Wiley: Chichester, UK.

Woldie, A. (2003) “Nigerian banks—quality of services” Journal of African Business 4, 69-87.