Two Effective Strategies to Support Cross-Organization Emergency Resource Allocation Optimization

Cross-organization emergency resource allocation optimization problem is essential to guarantee a successful emergency disposal, and it has become a research focus of modern emergency management. Generally speaking, there are two possible types of resource allocation scenarios: (1) if the emergency resources are overallocated, on the one hand, parallel execution of independent emergency activities can be supported and the emergency disposal time is reduced; on the other hand, too many idle resources may cause low resource utilization rate, high scheduling overhead, and high cost; and (2) if emergency resources are underallocated, this may lead to resource conflicts and the need for some emergency activities to wait for others to complete, and finally the emergency disposal time may increase. 0erefore, reasonable emergency resource allocation strategies are highly desired. To the best of our knowledge, there is no formal approach to support the cross-organization emergency resource allocation issue. To handle this problem, we propose a two-layered framework to facilitate the allocation of limited emergency resources to meet its time constraints with high efficiency. More specifically, a kind of Petri net extended with time, resource, and message information, denoted as CE-net, is presented to model cross-organization emergency response processes. Based on the obtained CE-net, the minimum resource requirements are obtained with corresponding algorithms. 0en, Minimum Execution Time (MET) strategy and Minimum Resource Consumption (MRC) strategy with their corresponding estimated execution intervals are introduced to facilitate the stakeholder to determine which strategy is suitable according to the timing requirements. A cross-organization fire emergency case is applied to validate the proposed approaches throughout the whole paper.


Introduction
e allocation of distributed emergency resources has been a challenging issue in the cross-organization emergency management area. An emergency is defined as a situation that imposes immediate risk to life, property, and environment, which requires urgent disposal and intervention to prevent its worsening [1,2]. ese disposals are normally organized as a group of collaborated emergency response processes charged by an emergency command center and several subordinate emergency organizations that need to work together to accomplish the whole emergency mission [3].
Generally speaking, cross-organization emergency response processes usually exhibit the following features (or requirements) that differentiate themselves from traditional business processes [1,[4][5][6]: (1) ere are close relations between emergency activities and resources. During the execution of an emergency response process, large quantities of resources, for example, ambulances, fire trucks, medicines, tents, food, and clothing, are badly needed. On the one hand, if the emergency resources are overallocated, parallel execution of independent emergency activities can be enabled to reduce the execution time; however, too many idle resources may lead to low resource utilization rate, high scheduling overhead, and even high cost. On the other hand, if the emergency resources are underallocated, this may lead to resource conflicts and the need for some activities to wait for others to complete, and finally the execution time of the emergency response process may increase. Consequently, reasonable emergency resource allocation strategies are highly desired. (2) ere are a lot of collaborations that need either messages sent by other organizations or resources shared among different organizations. Hence, effective collaboration modeling for this case is required. (3) Crossorganization emergency response processes are a real-time service where timeliness is critical to its mission success. erefore, time performance evaluation and optimization strategies are needed.
Modeling across-organization emergency response processes is a complicated and time-consuming work. In addition, optimized emergency resource allocation will benefit both successful emergency response process execution with high time performance and high resource utilization rate. erefore, emergency resources should be optimized and allocated properly at least from the two following perspectives: (1) minimizing emergency resource requirement as much as possible to achieve a high resource utilization rate and (2) shortening emergency response time as much as possible to achieve its crucial timing constraints. Note that this problem is different from conventional workflow resource scheduling [7][8][9][10][11][12], which aims at minimizing the application's runtime on a limited resource set. Differently, we try to propose effective strategies to support cross-organization emergency resource allocation optimization. To this end, we introduce a kind of Petri net [13][14][15] extended with time, resource, and message information, CEnet for short, to model cross-organization emergency response processes. Actually, the CE-net is an extension of our previous E-net model [1] to suit cross-organization scenario. Accurately, a time interval is used to predict the uncertain execution time of an emergency activity. In addition, emergency resources are divided as reusable and consumable ones; that is, the reusable resources can be reused by other emergency activities when released, while the consumable ones can be used only once and cannot be reused any more. e main contributions of this paper are summarized as follows: (1) a kind of Petri net extended with time, resource, and message information, CE-net for short, is proposed to model cross-organization emergency response processes; (2) a two-layered framework is proposed to support cross-organization emergency resource allocation; and (3) we present two effective resource allocation strategies, that is, the minimum execution time strategy and the minimum resource consumption strategy, to support the efficient emergency resource allocation decision-making based on the resource requirements analysis results. e remainder of this paper is structured as follows. Section 2 discusses the related work. In Section 3, a crossorganization fire emergency response scenario is given as a case to validate our proposed approaches. Section 4 investigates the modeling approaches for cross-organization emergency response processes using CE-net. en, minimum emergency resource requirements analysis is investigated based on the CE-net in Section 5. Section 6 introduces two effective resource allocation strategies to support the emergency resource allocation decision-making. Finally, Section 7 draws concluding remarks.

Related Work
In this section, we mainly review existing work related to (1) workflow resource allocation as well as emergency resource scheduling and (2) modeling of cross-organizational workflow and emergency response processes.

Workflow Resource Allocation and Emergency Resource
Scheduling. Workflow scheduling is a well-known problem whose main objective is to minimize the completion time of a workflow using a given (or limited) set of resources. Deelman proposes one of the most popular algorithms, called Pegasus, to schedule workflows on distributed systems [7]. It is built on top of the list scheduling approach and considers both communication and computation cost. Based on experimental evaluation, it is demonstrated that Pegasus achieves relatively good performance for most cases. Besides the list scheduling approach, other techniques, such as DAG-based scheduling [8], greedy randomized adaptive search [9], and critical path first [10], have also been investigated. More recently, Byun proposes a new algorithm named BTS for estimating the minimum number of hosts that are needed to execute a workflow within a given deadline to bridge the gap between workflow management systems and resource provisioning systems [11,12].
As authoritative emergency management experts, Tufekci and Wallace [16] consider emergency management as a complex multiobjective optimization problem and utilizing limited resources compromisingly is the best way to be adopted. Following their thoughts, emergency resource allocation optimization has been studied by many researchers in the past decades. A dynamic optimization model is used to find the best assignment of available resources to operational areas by Fiedrichet et al. [17]. In [18], by considering multiple disaster places and multiple resource suppliers, an optimized algorithm is proposed to solve resource collision problem for large-scale public emergency response. In [19], the problem of allocating multiple emergency service resources to protect critical transportation infrastructures is studied. Different modeling approaches, including deterministic, stochastic programming and robust optimization, are used to model various risk preferences in decision-making under uncertain service availability and accessibility. To find an optimal solution for resource deployment and dispatching, Kondaveti and Ganz [20] introduce a decision support framework built on rapid information collection and resource tracking functionalities. e equipment control structure presented in [21] enables decentralized and collective decision-making for equipment prioritization and distribution in response to disasters. More recently, by considering time performance, Wang et al. [22] discuss a negotiation strategy and a compromised resources allocation model for emergency response. e negotiation strategy can facilitate requesters to find out the demanded resources efficiently. In addition, a mathematical model is presented to compute the earliest start time of emergency response on condition of continuous requirement for resources.

Modeling of Cross-Organizational Workflow and Emergency Response Processes.
Van der Aalst first considers workflows distributed over a number of organizations in [23,24], where two important questions are addressed: (1) the minimal requirements of interorganizational workflow and (2) how to decide if an interorganizational workflow, modeled with Petri nets, is consistent with an interaction structure specified through a message sequence. In [25], Liu et al. propose a kind of interactive Petri net to model the message channels between different process-oriented systems, and the compatibility preservation of an integrated system with message interaction is revealed. Differently, Schulz and Orlowska focus on three aspects to support the execution of cross-organizational workflows that have been modeled with a process-view approach in [26]: (1) communication between the entities, (2) their impact on an extended workflow engine, and (3) the design of cross-organizational workflow architecture. A Petri net-based state transition approach that binds states of private workflow tasks to their adjacent workflow view is introduced. Its concepts are demonstrated by a scenario involving two workflow management systems. Jiang et al. [27] describe a timed colored Petri net and process-view combined approach to construct cross-organizational workflows, and a three-layered framework is proposed to realize the interoperability of cross-organizational workflows.
In [28], we investigate the application of process mining for workflow integration using a type of Petri nets extended with resource and message factors. A process integrationbased approach is presented to obtain the model for a crossorganization workflow based on the model mined for each organization and the coordination patterns among different organizations. More recently, we formally define several collaboration patterns, including message interaction pattern, resource interaction pattern, task collaboration pattern, and service outsourcing pattern, in [29]. Modeling and analysis of a cross-department medical workflow are effectively supported, and the correctness is verified by building the reachability graph. To cope with the crossorganizational characteristics of emergency response, we conduct the formal modeling and analysis of cross-organizational emergency response system in [4]. is work first introduces the formal model of emergency activities and identifies five kinds of interactivity relations during the cross-organizational coordination process. en, OTRM_-Net, a kind of Petri nets extended with time, resource message, and organization information, is presented to model the emergency response processes. Also, we further study its timing performance, resource conflict detection, and the reduction or concealment of inner emergency activities. More recently, we propose a top-down approach for model construction and correctness verification of crossorganization emergency response processes in [3]. For the resource conflict and resolution issue during the execution of cross-organization emergency response process, a novel controller design method is given in [5]. In addition, the privacy issue during the modeling of cross-organization emergency response processes is handled by a package reduction-based privacy protection approach in [6].

Summary.
Based on the above literature review, we can see that researches into (1) modeling and analysis of crossorganizational emergency response processes and (2) emergency resource allocation and optimization issue have drawn much public attention. However, the existing works have at least the following limitations: (1) emergency resources are not fully quantified (e.g., [2][3][4][5][6]); that is, emergency resource quantity is not investigated during the modeling and allocation process, which will inevitably lead to an inaccurate resource allocation; and (2) there is a lack of time description for emergency activities, based on which we can estimate the time performance of cross-organization emergency response processes when using a specific resource allocation strategy. To deal with these limitations, this work provides a two-layered framework to support optimized resource allocation for cross-organizational emergency response processes.

A Two-Layered Framework to Support Emergency Resource Allocation
In this section, we introduce a cross-organization fire emergency scenario that will be used as an illustrating example for the paper. en, we propose our emergency resource allocation mechanism.

A Cross-Organization Fire Emergency Scenario.
In this paper, a fire emergency scenario in [3] is adopted as a typical scenario. It involves the following organizations: police station, emergency command center (ECC), explosive ordnance disposal (EOD) team, fire brigade, and hospital. Some of the critical missions in this scenario are rescue of victims and disposal of the moving fire. is scenario includes the following steps: (1) e police station first receives the fire emergency call and then reports the emergency information to ECC. (2) e police rushes to the emergency site to perform its detailed disposal missions and then reports the site conditions to ECC. (3) After receiving the emergency information, ECC first establishes a temporary emergency command group and then makes and issues emergency plans to its collaborative organizations, that is, medical rescue instruction to a hospital, search EOD instruction to an EOD team, and fire rescue instruction to the fire brigade. (4) e EOD team rushes to the site upon receiving the search EOD instruction from ECC and conducts its specific disposal activities according to its emergency handling requirements and finally reports the EOD search results to ECC. (5) e fire brigade rushes to the site upon receiving the fire rescue instruction from ECC and conducts its specific disposal activities according to its emergency handling requirements and finally reports the fire rescue results to ECC.
Mobile Information Systems (6) e hospital personnel rush to the site upon receiving the medical rescue instruction from ECC and conduct their specific disposal activities according to their emergency handling requirements and finally report the medical rescue results to ECC. (7) After receiving all the feedback information from the hospital, EOD team, and fire brigade, ECC makes emergency summary and evaluation and finally does the file archive. (8) ECC arranges the media coverage for the whole emergency response, and, finally, ECC, fire brigade, and hospital do the media coverage together.

Cross-Organization Emergency Resource Allocation
Mechanism. To support the effective emergency resource allocation of cross-organization emergency response processes, a two-layered framework is presented as shown in Figure 1.

Layer 1.
Each emergency organization establishes its respective emergency response process based on the emergency requirements. en, each emergency organization submits its emergency response process to the ECC for further integration and evaluation. Next, the ECC integrates the response process received from its subordinate emergency organizations.

Layer 2.
e ECC first conducts the emergency resource requirement analysis in terms of minimum consumable resource requirement, minimum reusable resource requirement, and reliable reusable resource requirement. According the resource requirement analysis results, two strategies, that is, minimum execution time strategy and minimum resource consumption strategy, are obtained to guide the resource allocation. In this way, stakeholders can determine which strategy is more suitable according to the amount of available resources and expected finishing time. e scope of this paper is to provide decision-making information to support emergency resource allocation in a cross-organization scenario. In this case, emergency resources are like the public transportation vehicles, public communication devices, emergency personnels, and so forth.

CE-Net-Based Modeling of Cross-Organization Emergency Response Processes
In this section, we propose the formal definition of a Petri net-based model for the cross-organization emergency response processes, named CE-net, which is an extension of our previous E-net [1]. e CE-net is different from our previous models, such as RM_WF_Net in [29] and OTRM_Net in [4], as it emphasizes (1) the uncertainty execution time of emergency activities and (2) effective resource allocation strategy of cross-organization emergency response processes.
Definition 1 (see [13] Definition 2 (see [13]). A weighted Petri net is a 5-tuple (2) W: F ⟶ Z n is a weight function that maps an arc to a positive integer.
Definition 3 (see [23]). A Petri net Σ � (P, T, F, M 0 ) is a WFnet if (1) there is one source place p s ∈ P such that •p s � ∅; (2) there is one sink place p e ∈ P such that p e • � ∅; (3) each node x ∈ P ∪ T is on a path from p s to p e ; and (4) ∀p ∈ P, M 0 (p) � 1 if p � p s , and otherwise M 0 (p) � 0.
In a WF-net, the transition set T is used to represent the normal activities, the place set P is used to represent logic connection relation of activities, and source place and sink place especially represent the start and end of the process. Based on the classical WF-net, we propose CE-net by extending it with uncertain execution time, resource, and message information to suit the cross-organization emergency response process modeling demand. It differs from our previous RM_WF_Net in [29] as it involves the emergency activity execution interval.
P L ∩ P M � ∅, P L represents the logic place set, P M represents the message place set, and P R represents the resource place set in a Σ CE , and P R � P RR ∪ P CR , where P RR is the reusable resource place set and is the consumable resource place set; (2) T is the transition set of a CE-net, and it represents an emergency activity set; Mobile Information Systems (4) α: T ∪ P R ⟶ R. ∀t ∈ T ∪ P R , α(t) ≥ 0 is the minimum time to execute (or prepare) an emergency activity (or resource) t; (5) β: T ∪ P R ⟶ R. ∀t ∈ T ∪ P R , β(t) ≥ 0 is the maximum time to execute (or prepare) an emergency activity (or resource) t, such that α(t) ≤ β(t); (6) W: F ⟶ Z n is the weighted function, such that, t, r)). #req(t, r) represents the required amount of resource r to execute activity t, and #sent(t, r) represents the sent amount of resource r when activity t finishes (only reusable resources have this flow); (7) ∀p ∈ P, M 0 (p) � 1 if p ∈ P L ∧ •p � ∅, M 0 (p) � #num(p) if p ∈ P R , and otherwise M 0 (p) � 0. #num(p) represents the initial available amount of resource p. e firing rule of a CE-net is the same as that of a traditional Petri net. Given a marking M, ∀t ∈ T, t is enabled under M if, ∀p ∈ • t, M(p) ≥ 1, where p ∈ P L ∪ P M ∪ P R . Firing an enabled t removes a token from each place in • t and deposits one to each place in t • . All properties, such as reachability and boundedness, can be defined similarly. e main differences between an CE-net and a Petri net are the following: (1) the CE-net is a special type of Petri net Mobile Information Systems extended with message place set (P M ) and resource place set (P R ); (2) a transition in CE-net is associated with two time functions to represent its minimum and maximum execution time; and (3) a weighted function is introduced to represent the amount of required or sent resources when an emergency activity starts or ends.

Modeling of Cross-Organization Emergency Response
Processes Using CE-Net. Modeling of cross-organization emergency response processes involves the following steps: (1) modeling emergency activities with CE-net; (2) modeling control structure with CE-net; and (3) integration of control structure model with those activity models.
In a CE-net, an emergency activity model is shown in Figure 2, where p ready is the ready place, p end is the end place, P resourceReq and P resourceSent are resource places which mean the required and sent resources, p messageReq and p messageSent are required and sent message places, and α(t) and β(t) are the minimum execution time and maximum execution time, respectively. To distinguish the logic, resource, and message places properly, a logic place is drawn with a normal circle, a message place is drawn as a circle with dashed line, and a resource place is drawn as a two concentric circles with full line.
It is worth noting that the control structure of a CE-net, denoted as (P L , T, F L , M 0 | L ), is a standard WF-net, where M 0 | L is the projection of M 0 on P L . erefore, its basic control structures, including sequence structure, concurrent structure, choice structure, and loop structure, can be modeled in the same way as that demonstrated in [29]. According to the emergency response descriptions in Section 3, emergency activity information, including activity ID, activity name, required resources/messages, sent resources/ messages, of the Police state, ECC, EOD team, fire brigade, and hospital, is shown in Tables 1-3, respectively.
It is worth mentioning that we use multisets to represent the required resource set and the sent resource set of an emergency activity. M(R) is the set of all multisets over a set R. For some multiset m ∈ M(R), m(r) denotes the number of times element r ∈ R appears in m. For example, m � {a 2 , b 3 } is a multiset over {a, b}. It represents that element a appears two times and element b appears three times in m. e ordering of elements is irrelevant for multiset.
Using the detailed modeling approaches in [29], a CEnet is obtained as shown in Figure 3, which represents the overall execution process of the cross-organization fire emergency response processes in Section 3.
It is worth noting that there are five resource places that correspond to five kind resources. For graphic simplicity, some resources may have more than one resource place.

Reduction Rules of CE-Net
Based on the modeling approaches in last subsection, a CEnet can be constructed. Unfortunately, the CE-net may contain an excessive number of places and transitions, which will lead to an inefficient analysis and troublesome understanding. Hence, two reduction rules are introduced to reduce the model scale while maintaining the structure, time, resource, and message invariant.

and their timing constraints are [α(t i ), β(t i )] and [α(t j ), β(t j )], respectively. en, transitions t i and t j can be merged to a new one, denoted as t ij , such that
. Rule 1 shows the reduction rule for sequential activities that do not require any messages and resources, and an example of Rule 4.1 is shown in Figure 4, where t i and t j are merged to t ij .
Rule 2 shows the reduction for two concurrent activities that do not require any messages and resources, and an example of Rule 4.2 is illustrated in Figure 5, where t i and t j are replaced by t ij .
We have the following explanations for reduction rules: (1) we only introduce the atomic reduction rules, and some advanced composite rules can be realized on top of these basic ones; (2) we only introduce rules that suit the sequence and concurrent structures, while choice and loop structures are not considered because their reduction results are usually not deterministic and can cause property changes compared with the original model; and (3) the firing rule of a transition obtained by reduction is the same as that of a traditional one; that is, the firing rule of a reduced CE-net is the same as that of a Petri net.
In the following, we show how to use our reduction rules to reduce the CE-net in Figure 3. t 11−12−13 is obtained by merging transitions t 11 , t 12 , and t 13 using reduction Rule 4.1 e CE-net of the cross-organization fire emergency response processes after reduction is shown in Figure 6. To give a comparison, Table 4 gives the number of transitions, message places, and resource places of the CE-net before and after reduction. Based on the comparison, we can clearly see that (1) its scale (in terms of the number of transitions and logic places) is much smaller and (2) the collaboration elements (resources and messages) stay invariant.

CE-Net-Based Minimum Resource Requirement Analysis
In this section, we discuss the minimum resource requirements of cross-organization emergency response processes based on the CE-net. During this procedure, we analyze reusable and consumable resources separately. For simplicity, we first redefine two vector operators, "<" and "≥." Let X � <x 1 , x 2 , . . ., x n > and Y � <y 1 , y 2 , . . ., x n > be two n- Assume that the available consumable resource vector and available reusable resource vector of cross-organization emergency response processes are denoted as R AC and R AR , respectively.

Minimum Consumable Resource
Requirement. e minimum consumable resource vector is denoted as R MC � <q(r 1 ), q(r 2 ), . . ., q(r n ) >, where (1) r i (i � 1, 2, . . ., n) refers to a kind of consumable resource and it is modeled as a resource place p ri in P CR and (2) q(r i ) represents the number of r i . V MC can be computed by taking as input a CE-net based on the following algorithm. e complexity of Algorithm 1 is Ο(|P CR | × |T|), where | P CR | is the number of consumable resource types and |T| is the number of emergency activities. For real-life emergency resource management, the cross-organization emergency response processes will break down because of shortage of consumable resources if R AC < R MC .

Minimum Reusable Resource
Requirement. e minimum reusable resource vector is denoted as R MR � <q(r 1 ), q(r 2 ), . . ., q(r m ) >, where (1) r i (i � 1, 2, . . ., n) refers to a kind of reusable resource and it is modeled as a resource place p ri in P RR and (2) q(r i ) represents the number of r i . Algorithm 2 shows how to compute V MR by taking as input a CE-net. e complexity of Algorithm 2 is Ο(|P RR | × |T|), where | P RR | is the number of reusable resource types and |T| is the number of activities. For real-life emergency resource management, the cross-organization emergency response processes will break down because of shortage of reusable resources if R AR < R MR .

Reliable Reusable Resource
Requirement. Even though we have R AR ≥ R MR , resource conflicts may still exist during the execution of cross-organization emergency response processes because of resource dependency and limited available resources.
is kind of conflicts may delay the execution time of the emergency process. erefore, the reliable reusable resource vector of a CE-net, denoted as R RR � <q(r 1 ), q(r 2 ),. . ., q(r m )>, is introduced, where r i (i � 1, 2, . . ., n) refers to a kind of reusable resource and is represented as a resource place p ri in P RR . Algorithm 3 shows how to compute R RR by taking as input a CE-net. e complexity of Algorithm 3 is Ο(|P RR | × |T|), where | P RR | is the number of reusable resource types and |T| is the number of emergency activities. If R AR ≥ R RR , there is no resource conflict during process execution; that is, potential resource conflicts are avoided as sufficient resources are provided to support parallel execution of activities in resource dependency.

Theorem 1. e proposed approaches to analyze resource requirements of cross-organization emergency response processes on the basis of CE-net have Ο(m × n) time complexity, where m is the number of resource types and n is the number of emergency activities.
Proof. To analyze the resource requirement, three kinds of resource metrics, that is, the minimum consumable resource vector, the minimum reusable resource vector, and there liable reusable resource vector, are needed. eir calculation algorithms are implemented in Algorithms 1-3, the complexity of which is no bigger than Ο(m × n), where m is the number of resource types and n is the number of emergency activities.
erefore, the proposed method to analyze the resource requirement has its Ο(m × n) time complexity.

Two Effective Resource Allocation Strategies
In this section, we propose two optimized resource allocation strategies, that is, the minimum execution time strategy and the minimum resource consumption strategy. e former pursues time efficiency of cross-organization emergency response processes, and the latter focuses on high resource utilization rate. For each strategy, we estimate its corresponding time performance, based on which the stakeholder can determine which strategy is suitable according to the timing constraints. Before rendering the detailed strategies, we first introduce the time performance estimation and resource conflict detection approaches. Alarm receipt t 2 Report emergency information t 3 Rush to the site (police) t 4 Deal with the scene t 5 Evacuation t 6 Rescue the wounded t 7 Alarm receipt t 8 Search the suspect t 9 Establish temporary emergency center t 10 Make and issue emergency plans t 11 Emergency summary and evaluation t 12 File archive t 13 Arranges media coverage t 14 Do media coverage (together) t 15 Rush to the site (EOD team) t 16 Search the EOD t 17 Report the EOD search results t 18 Rush to the site (fire bridges) t 19 Fight the fire t 20 Recovery the site t 21 Conduct mitigation operations t 22 Report the fire rescue t 23 Rush to the site (hospital) t 24 Shunt the wounded t 25 Treat the severely injured people t 26 Treat the slightly injured people t 27 Environmental quality detection t 28 Report the medical rescue p m1 Emergency information p m2 Site conditions p m3 Medical rescue instruction p m4 Fire rescue instruction p m5 Search EOD instruction p m6 EOD search results p m7 Fire rescue results p m8 Medical rescue results In a cross-organization emergency response processes scenario, an emergency activity starts to be executed only (1) after the termination of all its preactivities, (2) after receiving the required messages sent by other organizations, and (3) under the condition that all of its required resources are available and sufficient. In this subsection, the minimum execution time of a cross-organization emergency response process can be obtained.
Without considering resource factor, if each emergency activity is completed in its minimum execution time, the earliest time to start activity t, denoted by T e1 (t), is as follows: (1) Without considering resource factor, if each activity is completed in its maximum execution time, the earliest time to start activity t, denoted byT e2 (t), is as follows: (2) e minimum execution time of a cross-organization emergency response process can be found if no resource conflict occurs. However, resource conflicts are inevitable during the execution of a cross-organization emergency response process. erefore, resource conflict checking approach is investigated here.  Figure 3: CE-net of cross-organization fire emergency response processes.

Mobile Information Systems
In the following discussion, we use T start (t) and T end (t) to represent the real start and end time of an emergency activity t. We have two types of resources, reusable and consumable ones. e former one becomes available and can be reused after being released, while the latter is consumed during execution and cannot be reused. For this reason, resource conflict mentioned in our work is essentially caused by the reusable resources. If a conflict is caused by consumable resources, the only way to solve it is to add more such type resources.
According to Definition 5, an algorithm to obtain the resource dependency in a cross-organization emergency response process is presented as follows.
In Algorithm 4, the complexity of Step 2 is Ο(|T| 2 ). erefore, the complexity of Algorithm 3 is Ο(|T| 2 ). By executing Algorithm 4, the resource dependency set of the emergency response process scenario is obtained: DependencySet � {(t 2 , t 10 ), (t 4 , t 5 ), (t 4 , t 6 ), (t 5 , t 6 ), (t 18 , t 23 ), (t 17 , t 22 )}. Here, if two activities have resource dependency; that is, they share same emergency resources. However, this does not necessarily mean that resource conflicts will occur between them. Only when these two activities need to be executed simultaneously will resource conflicts take place. In the following, the resource conflict between two emergency activities is formulized. Definition 6. ∀t i , t j ∈ T(t i ≠ t j ), t i and t j are in potential resource conflict, denoted as t i ⊗ t j , if (1) t i Θ t j and (2) [T start (t i ), T end (t i )] and [T start (t j ), T end (t j )] are overlapping.
Definition 6 defines the potential resource conflicts, based on which we present an algorithm to check resource conflicts.
In Algorithm 5, because Ο(|ConflictSet|) ≤ Ο(|T|), the complexity of Step 2 is Ο(|T|). Hence, Algorithm 5 has its computational complexity Ο(|T|). By executing Algorithm 5, we can obtain that ConflictSet � {(t 4 , t 5 ), (t 4 , t 6 ), (t 5 , t 6 ), (t 18 , t 23 ), (t 17 , t 22 )}. However, even if t 4 and t 5 are in potential conflicts, t 4 requires 2 public communication devices, and t 5 also requires 2 public communication devices and if the total number of available investigators in this case is less than 4, conflict occurs because of the competition for public communication devices. If the total number of available investigators is more than 4, t 4 and t 5 will no longer be in conflict. Based on the aforementioned analysis, we can see that whether a cross-organization emergency response process can be accomplished in its ideal execution time    Input: Σ CE � (P, T, F, α, β, W, M 0 ). Output: R MC . (1) / * Step 1: initialization * / (2) Step 1: sum ⟵ 0, R MC ⟵ 0.

Conclusion
Efficient emergency resource allocation decision support is of vital importance for cross-organization emergency management. To some extent, this will influence emergency resource utility rate and the whole emergency mission success. In the work, we first propose CE-net to model a cross-organization emergency response process, based on which emergency resource allocation decision-making strategies, including minimum execution time strategy and minimum resource consumption strategy, are presented. According to the available emergency resources and emergency time constraint, certain strategy is selected by the emergency manager according to their specific requirements. It is proved that the minimum execution time strategy can ensure the global emergency response process execution without resource conflict or block, and therefore the performance is optimal. e minimum resource consumption strategy can guarantee the whole emergency to be finished with the least emergency consumption, and, in this way, the resource related cost is reduced. However, there may exist some resource conflicts during real-life emergency process execution when we choose the latter. To resolve these conflicts and maintain a success execution, efficient resource conflict resolution strategies are needed. erefore, resource conflict resolution strategies with corresponding controller design approaches will be our future work. In addition, it would be interesting to discover such emergency response process models from historic emergency response logs by using process discovery techniques and advanced learning algorithms to realize data-driven emergency decisionmaking [38].
Data Availability e data used in this manuscript come from an emergency management branch, and the authors cannot release all information at the current stage for privacy protection.

Conflicts of Interest
e authors declare that they have no conflicts of interest.