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Cost Sharing for Capacity Transfer in Cooperating Queueing Systems

机译：合作排队系统中的容量转移成本分摊

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We study the problem where independent operators of queueing systems cooperate to generate a win-win solution through capacity transfer among each other. We consider two types of costs: the congestion cost in the queueing system and the capacity transfer cost, and two types of queueing systems: M/M/1 and M/M/s. Service rates are considered to be capacities in M/M/1 and are assumed to be continuous, while numbers of servers are capacities in M/M/s. For the capacity transfer problem in M/M/1, we formulate it as a convex optimization problem and identify a cost-sharing scheme which belongs to the core of the corresponding cooperative game. The special case with no transfer cost is also discussed. For the capacity transfer problem in M/M/s, we formulate it as a nonlinear integer optimization problem, which we refer to as the server transfer problem. We first develop a marginal analysis algorithm to solve this problem when the unit transfer costs are equal among agents, and then propose a cost-sharing rule which is shown to be in the core of the corresponding game. For the more general case with unequal unit transfer costs, we first show that the core of the corresponding game is non-empty. Then, we propose a greedy heuristic to find approximate solutions and design cost allocations rules for the corresponding game. Finally, we conduct numerical studies to evaluate the performance of the proposed greedy heuristic and the proposed cost allocation rules, and examine the value of capacity transfer.
机译：我们研究了排队系统的独立运营商合作通过彼此之间的容量转移产生双赢解决方案的问题。我们考虑两种类型的成本：排队系统中的拥塞成本和容量转移成本，以及两种类型的排队系统：M / M / 1和M / M / s。服务费率被认为是M / M / 1中的容量，并且被认为是连续的，而服务器数量是M / M / s中的容量。对于M / M / 1中的容量转移问题，我们将其表述为凸优化问题，并确定一种成本分摊方案，该方案属于相应合作博弈的核心。还讨论了无转移成本的特殊情况。对于M / M / s中的容量转移问题，我们将其公式化为非线性整数优化问题，我们将其称为服务器转移问题。当代理商之间的单位转移成本相等时，我们首先开发一种边际分析算法来解决该问题，然后提出一个成本分摊规则，该规则被证明是相应游戏的核心。对于单位转让成本不相等的更一般情况，我们首先证明相应游戏的核心是非空的。然后，我们提出一种贪婪的启发式方法，以找到相应的游戏的近似解决方案和设计成本分配规则。最后，我们进行了数值研究，以评估所提出的贪婪启发式方法和所提出的成本分配规则的性能，并检验能力转移的价值。

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